{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "sns.set(font_scale=1.5)\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>sex</th>\n",
       "      <th>smoker</th>\n",
       "      <th>day</th>\n",
       "      <th>time</th>\n",
       "      <th>size</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "      <td>Male</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "      <td>Female</td>\n",
       "      <td>No</td>\n",
       "      <td>Sun</td>\n",
       "      <td>Dinner</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   total_bill   tip     sex smoker  day    time  size\n",
       "0       16.99  1.01  Female     No  Sun  Dinner     2\n",
       "1       10.34  1.66    Male     No  Sun  Dinner     3\n",
       "2       21.01  3.50    Male     No  Sun  Dinner     3\n",
       "3       23.68  3.31    Male     No  Sun  Dinner     2\n",
       "4       24.59  3.61  Female     No  Sun  Dinner     4"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = sns.load_dataset('tips')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "bill = data[['total_bill']]\n",
    "tip = data[['tip']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=False, n_jobs=None, normalize=False)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "lm = linear_model.LinearRegression(fit_intercept=False)\n",
    "lm.fit(bill, tip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.1437319]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.54192789]])"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lm.predict(np.array([31.60]).reshape(-1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.scatterplot(data['total_bill'], data['tip'])\n",
    "ax.set_ylim([0, 11])\n",
    "ax.set_xlim([0, 53])\n",
    "fig = ax.get_figure()\n",
    "fig.savefig('no_fit.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pCx8AHDx4EEOGDEGLFi089hUEAZ9++il++eWX0EuZQISrZHYiE4gJJ9RmHvfzTRnV2e8zDdW1WdZ7IyaWZQA+vPdB5ePal8oq8co/vo66uTXYcUXbZBzt69eF3zyOsrIyDB8+HOXlgcUEi6KIPn36YP369SETMFTESh5HqL8wFM9eHlCRwkALGQaK+/na5xpw320dsWLrV16faaiuLapYXLhaJbvOo2PzkdNEC8Ye2HXqKwvHsbhWZcNzbt/bx8d3x6Z3vkfJGVPE62TV/t4HO65Qfx+CpSHXj3oeR3p6Ol544QUcO3YMoihi1apVGDJkCNq3b+/lIizS09Nx++23N1jgRIaa6YSeQExFoTYRup+v5IwJf9tzAlNGdUbLHL3HMw3ZtUVg92cnMWVUZ+i1apRX2bD7s5OYelfngK9TX1l4XkBjt+/tfy+US0qj3uMJIcGOK9om42hfvy7qlGHAgAEYMGAAAEeRw3HjxqFr165hFyyRocSt0BKI+S/UJsLa5ys5Y8K6ncekN0bez771vbYKwPihHXz2BAn3fXB+bzmOxbqdxxRlbg12XNE2GUf7+nXBLVq0aFGgOw8ePBjZ2dlhFCd8VFdbodAK2GFFp0tCVZW17h3jEOfYVSyDgrwcHC25jEqzXZpQdWpOakYWyD7BEMz5QnVtURShTVJhYEEuRg1og8EFzWV5FJG6D6G+l/Wh9vc+WJmiPYaGXD9Uv3mGYaDVarx/FkytqlgmVnwcoYZ8HI6xRyOqSq3hYOUBXhDAsSw0HGCzel8/hvravp57pO5DNCOCOI4Fo+Zgtthl106UqKqo+zgIIl4IxPwXShMhx7EoLbcGHOQQKfNkpO6D+zk4MI4JkGHCPgG7gksOeL3vwYwr2ibjaF/fH5SbQxBhwFcynj26YkUc50RetPoAphZ/iKLVB2CqsoHjwjP10H2PDKQ4CCIM+IuKSSQiPZHTfY8MpDgIIgzEQrtZjmMhcizsDAORY8OyCoj0RB4L9z0eIMVBEGFA6e1mI2VCivRErvT7Hi9QVFWcQ1FV0Rt7NKNy6hp7pDKjo1E6w1dUVaJAUVUEEcPwvAAVxwIs4zDNsAxUHKuISSxSmcnRqITA8wIy0nW4Yi5XXDRSvECKg4gK0Y6RD7ccHMeCBwMzL+D81Qps2fsDTOVmxRSqi2RmspLDSon6QYqDiDhKqfwZLjm8nffRsfn4254Tiumt4vQF+CpPQhD+IB9HnBNtO783wmlfd19BJCepINp4n0ogXHL4Ou+UUZ3x/KaDWFs0CKow/OyCGXvt/ePNF6DE732kIB8HEZeEy74e7AoiXHL4Oq9eqw6bOag+qycyIRH1JebCcWfOnIkhQ4ZEWwyiAQQTohlMrkFdyWa1z6VRs2EJFfU1PrPVHrbQUMqYJiJJTCmOnTt34oMPPoi2GEQDCTTWPthcA98rCEedJIsgYu2OY9K5rpdbseihX4c85t/X+Frd1ChsfhzKmCYiScyYqi5duoTnnnsuZsu6R4radutI+HWCtZW7h2iCARgwsPMibABUGg4ML4LnBdlbdPtcA0YPbAuLjYfIJQFgYBcEefVTH5FCpvJqXK+wIS1Vg0l3dIJeq8G+Q2fx3KaDWDyjb52hog0ZHy+I0KhZCDxgtdXI6yMkN5hquh7PQOH9G+pDPPtgYp2YURwLFixAnz59kJSUhCNHjkRbHEXizc694MGeSEtWRaAaaXCRSc4ch2uV8najs8flw6BPgk7NwVLzFu3eetWgT8bE2zti+RbPNqyAZ6TQ3Pt7wGoVpMZCmYYUzJ1YgLOXKlByxgS7IEAlij7t/A0ZHwMgiWNhCqBKrlrD4Wq5FcVu+xVNKkQTvSYg5RFvUVJKibwjvBMTpqpt27bhu+++w1NPPRVtURSNNzv3sxu+DKuduyG2dTsgKQ3nscu3fIVLZVWww/UWPXpgW6mP9uiBbSWlUft67m/6a4sGofiRvqiqtuPlzUdl+y957RBGD2xb80bu33/SUN9BoMdbeUhKw7lf8aaDCHDB4TH2F2f3j+lJlnw2ykbxK45z586huLgYxcXFSE9Pr/d5fIWVxROXTVVe7dxgGGRk6BV3TV/HJmtUAMOgSZpjxVRtsUv76bXqgK9nKjdDo+a87p+WqkHRpEKs3fEtvvzukrQ6a5HdCKybc7yh9zTQ4y9crfTuoxBF5ITp2SmZUHyXw/WdjwXCPXZFKw5RFDF//nwMGDAAw4YNa9C5EiKPg2O92rkhiuGLaW/INX0ca7baAVFEaWkF0pJV0CWrpf3Kq2wBX89oTIXZYve6f5O0FElpAK7VmUcOR0PvaYDHcxzn3UfBMPV6djGfx9DA+x7z428AkcjjULSp6o033kBJSQnmz58Pu90Ou90u9dt1/3/CgbdongUP9gzr20FDqpGqADxZ69jZ4/KRla6Vjud5ASqIWPTQr/H0lJ7IaJyMefcXBHQ9lmWQoma9ygdGlJSGE29RSPUZn3vYLwMmoMgtDQcU1bpO0aRCaDh/dzB+oSq3ykbRmeP33XcfDh486PPz4uJi3HPPPQGdKyFWHPCMRGnSWIvS0oqIXjOQ6BfnMe5RVSwLqDhGiqpyotZwsjasPfOyMPnOTmAYBiwDn9dzvnl5k88OBJw1Hsz4vDl1n5xUiDS9xhVV5eP4hkRV+Rp7pAhHBFRDzkkrjvCuOBStOE6dOoXKykrZtlWrVuHEiRNYuXIlmjVrBoPBENC5EkVx1EaJP6BgI2ZEjkPR6v1eJvm+YHjfE6u/sYcraidS5crrIpLPXYkRUEr83keKhC850rp1a49tjRs3hkajQefOnaMgEREKfEXM+Cr+xwuCj+Q2od5f4FCU+3Z/I1axLFjOkasRiXLlSiLY50nEPvH6XSYUTLA1ojjWu6OUY1nAz4qjTjkaUKvJ21v27HH5EAQx7hLx6iJSvT0I5RBzz3Xx4sXRFiGhCYUt21uWc8+8LHAsC5ERwbGOzGrnm3ySmsHTD/0al8uqkKxRwWy1IzNd6/AB8L7l8iY7X5NxzrIMNGoWdpvokYEeiK+h9lu2QZ8Mq41HtlGHZ6b2xqZ3jkthvrGciBcIKh+KXdVAxR6rJELGe8wpDiJ6hMqWXTvLuWdeFsYN7YC1O77FmMHtYLHysszwRQ/9Gna7gDXbv3U5nB8ohFDzBu9LrsaNXW/4HMfiWpU8S33e/QXY+kGJbIJvkpaEK9ctdWZwu79lu2e2u2enT727MyD6dt7HCywHzB6XL3tms8flg+UAIcH0hhL9PeFA0eG4RPgJZfXZQHH3L6xfMBhT7+oCq43HxNvyUF5p9cgMv1RWhec2yq/73EbXdX3Jdb3SIpO9dpb64r8ewqCCFrJjLDYxoAxu9wq47pntzmOWvHYIEBkwvOA3AivQe69krDYBr717AlNGdUbxjD6YMqozXnv3BKy2+JkoAyVRMt5pxZHARLN/hbNWlanSdf0lM/siWaPyuIa3be7X9SWXze7wYXAcK9W9qr2PvqbGleucgTni3VdNvrLZBUGErzSMeHoz5VgGpnIznt/kCp2Pd7+OLxLF3xObrzhESAj27SiYPhr1uf71CqvDf1HrGt62uV/Xl1xqFStN0OeuVHjdp7zKVuucvnp0uH4qThu2XqdG8Yy+yDRovR7D+vl1xdObKSXruQj1b0SpkOJIYILt4RDIBBGU+YWBZN6YP6kQB7+7AL1Og9nj8mXXaJyahDn/c4ts25Nu1/UlV5ouSZqgt+z9AY+OlZ933v0F+PDQz7JjktSMRwb3/EmFUHEMOM6liIpWH8DkZ/ehaPV+WGx2jwz4uibOeOqf4VFcckafmFw5hYJEUaKKTgAMJZQA6El9ktX8RYwEY37xtu+jY/Nx5MRFjBrwK0d/DhuPq9er8cnRXzC8d0uUV1qlqKqsdC10ak52bTsAQXAkLoERkaTmYLEJuFxWhfIqGw5+dwGFeTnQa9XIMKT4jaqyCYDNLuD81Qps2fsDTOVmh8Ndr8H/vuKZjLh0Vl/wvBhwJE24EwUDTQKL1wigaCYARvueJnzmeCghxeFJqO3sdU2G8h8U6zUb/NlpvZHEOrr1TS3+EIDjDc7ZT8Pbeb2Np8uvmuC3A9vheqUF1yus+PDQzxjZrw3+tucETOXmOidoX2N5fkYfTHlun8f+a4sGQRXET8lnJJg+CRzEepcacRLI5BFPfpbaUOZ4AmeOE+ElFNnTsvP5Mb8k1Zqklszs67Nsth2Q+oEb9MlolpkakMPRaZYy6JMxoncrLFz7uWw1s/uzkxg3tB0M+uQ68yp8jUUQEJIEP+e9X/xIX2lls2b7tzCVm4Nq4OQNjmNhKjfDzjB+n2ldGd/RfnMmlAspjgSnodnT7hOLhmOkyX70wLbQa9UwW+0OkxAvejjCvU3A/z1/A+t2HsOTkwrx7PTeuGKqxqWyyoAma+dkP2VUZyx57ZBsQlyx9StMGdUZTTP0SGIDKMLooxWrimVC1mmP5wWIHIenXv1cdp3iTQcddbiCPB/gvoo4UOcqIhhFH0+rEaLhkKkqzgnXkp3jWFTaeFxyy+bOStdCpWJxxVSNXZ+exKCCFshMT0FaqgaCAFisPDjOUWrcbLNDzXGyDOvHx3eHIIpgGQYsCzRprMXVa9Ww2nikJKuw9LXDrqTAqb9GsloFe02vcQ3HwFZzDbWaxQt/O4KSMyapV7leq0Z6o2SkJHOSX4NlGa/VeJ3jq50w+OSkQjSuCd8N1Zu4nWEkk5w77qYvX1nx3mQIxnfib18g8OrB4SKYcdcmI0OPsrLKhFwxkamKUCwix8BUZpFlc88el4+mGanY9elJjOzXBrs/O4kxg9vhUmk1/vT3I7L9kjQc3njvBMYP7YCpd3fG+SuVUKtZLH3tsNRXvGjVfumYx8d3d2QjMwyym2hxvdyKRWtdnxdNKsSWvf+RlNDscfn46PBZ3HpLc1lGt7f9nD3Oa08qajWL6aO7SIpRrXZEiLn3E7cDsAgiOI6tZ/kV/3W4fJVpV6tZLPrLFx6rAV/5Kt7yCPz1KQ/mPOHA27gXPfRr2GyCTJn7WgUJgkgrpjDCLVq0aFG0hYgE1dVWJMbaSo5Ol4SqKmvIz8uDwfNu2dyVZjuOn7yK3/RoDoM+BWu2f4PfDmwHOy/glX987bFfl181QYucNCzf+hUGF7SAqdwsZYw/fHcXrNn+jeyYYz9dRec2GVj95jfo27Up/rjhS9nnX5Vcxm8HtsNnX5+TrjF9dFeZycrXfh1bpUOfmgQVy0BgGYfJiWGxYfdxvPF+CT48dBafHD2HQ99fwsCCXDCiKE1si/7yBbZ88AO+OH4BBXk50CapgmowplGzuOXmbHxVchmVZruk3PTJHARehMAykoJwjuFoyWV0bJWOPZ//V7ZtYEEuWIbBF8cvoNLsygjJNKRgSKFDbndEUYQ2SYWBBbm4o28rDCnMlRQow7EBnycceBt3j45Z+JNb/3j3cdeWySaKMhOgv33jjVD95hmGgVar8foZrTiIeiH4cR6npWpkWdne9kvWqJCscWVY39TE5QD3lYmdlqrBo2PzUWm2BZQFruKYgPZz9DiHLIvd6VC/Vm5FyRmTtK/zjTtUpcRtVh5N9BoUz+jrtaiiLz9EskblsY0XRCQF6YPx5ePytxqJRPkpb+Ouq4KAOzZ74pW3jyR0D4l64bMiKsfAoE+SsrLVKu9OZrPVDptdlDKsObjO56uveGqKBiu2foVxQ9t5/dw9C7xnXpa03d9+TlkgMh6KwOlQd5bScHfIh7K0hM3Ku03evFTxF/DtpDdb5TnmTtmc0Vovzu4Ps8Veb9t+qCPugsXbuJ0VBAKJaFOrfJkAE68MSjigzHEiIDiOBavhINRkhYOBRy/tJycVghNFqc/3h4d+hl6nwRP3yrO+Z4/Lh16nwYeHfpbeYjmImD+pEHcPaI2WOY08sm9nj8vHiq1fwVRuRqNUjdf+3O5Z4A/c0Qnrdx33yBafX2s/Z49zwUeNqrRUjexYp1KIVGkJb5nIT04qRFa61mNc7n3aDfpkqETRb5HFuuB5AQwvNPg89cHbuLPStQFn6KfpkhIigztaUFRVnBOKCAtnBJWp3CIrnf3kA4VIS/XeS9u9pzjHsuAFETzveHPlOAa8INi7+JwAACAASURBVHiUHNckq6SS5gZ9MsYNbYebmqRCo2LBsgwsNkckFMc5Jm73rG8Nx8DGA3bB0btcFIGHnt8ni6oqr7LhV83TAMG1nzOqyncPcqcJqf5Z8g2lPtFF8ZAAR1FV9YMyx0MIKY76I3IszlwqlyKonGQaUrB4Rt+QNevx11tcBc+Q2fqey1uf8vooAiUnyMWD4mgIiTx+CsclGowgiBA5tkGTGy+IPh2TNl5AMseGZML0VdLcxgsot9iDe5tnRDw6Nl8Wivvo2HyA8f7yUB+bfkOSJ+uDkhUVkViQ4ohjOI7Fzxdv4Nma0NVgzCm160r5ckyev1qB3Cx9vbKcPa7pw+HO12SdBxWxJAK7PzuJKaM6S2aq3Z+dxNS7Ovs8JBhFEOlJPJ7rShGxBznH4xg7ICkNwLPng68S6M6s6bU7juG/F8pxrcKC3Gy9h7Px8fHdsWXvD+AFRwa0UONAD6STHcexgIqDnWFrjlMhWcN6OL3n3V+Atz/+UQr1DbRkuwrAhOEdsW7nMRStPoB1O49h/NAOIXlTci+tPrX4QxStPgBTlS2sHfziqX9HvBAvHRzrA6044ph61yICg7/v/Q9G9msjmXp65mVh4u03e2RSN9ZrcO5KOZ5Z92WdmdhOOI7FtWqb1A7WeVxjfRIyDcl4bnofyZn+9sc/Yt+hs8g0pECEiKLVnwf0xs3zAlpkN5JMTxo1C4EHLIJQ7yxvJ6HK4QiGROksFysocQUoiiKuV1px4boZ/zl5FRdKq3ChrAqXyqowvGcuBnZvFrJr0XcujvGVA8CxjN/JjxcEDCpoIeujPaigBZ5xy+R1nuv/pvbGy5uPSudYvuUrTB/dxa/5yg549BB3HpesVuHF14/gvts6yvwT8ycVYv2u40FN1izr6PmdxLEwlVtD9iOPxiTu71lSXkLkicbLg3Rt3uELvFBahYtllQ4FUfP/1RaXgTVJwyEnXYu2zdLQKqdRSGUgxRHHqAAseLCnh4+jdi0i95BVEY63KWf2txNf2dzl1a7Maue2ZI3K7yTqLxuaF0SYys34254Tkn/CbLUjTa/Bl99d8iqvqg7nfKh/5NGYxKOdyU3IicTLQ6XZVqMUKnGxRjlcKKvCFVM1BLdgWIM+CTlGLXrn5SDbqEXH1k2QomLQOFUDhgmPGiPFEcfUNte4O3E5ztXvovbb/aKHfo201CTZ5Ogrm7uiVk0cZ1azv0nUXzY051Yy4/lNB6VoqMtlVT7lrWv1EOofeTQm8WhnchNyQvXyIIgiyq6bcaGsZtVQWonzNf+94VbhQMUxyDJo0SxDh4IOmcgxapFj1CLLoEVKkvxbHIlQZMrjiHN8fYmcNlpTudlrfsbSWX1RdsOCrR+USOXRIUI2WXqr0urPx+FwJjIQAdyosHr1caRp1eBtAuxgcPV6Na5XWLH9Xz8CACbe3hFWG+9VXm/lvp1jFzkWa3ccw6CCFlKE1YeHfsbUuzrXu0S40kNjEzmPAQj/+IP1cVhqWhBIKwinoiirgs3u2l+XrEJOEx1y0rXIMeqQXaMgmqQlOyomBwAlAIYQUhyecBwra9EKuMxALXP0UHGOMFynYuiZl4XJd3YCA0e/DKnEBRgpE1vNsRAhemST184+nz0uHwwYNNYngWUZlF539PBwTube+lS0zzXg9xO619m/ovbY1RoOV8utKHb7kQfSZU/pysEfpDjCP/7a3w9OFGG6YZZMSu4mptIbZuk4hgEy0lIkpZBj1CE73fH/eh/VaIOBEgABCIKArVu34u9//zt++eUXGI1GDBo0CLNmzUJqqvdBEYHhbrK6bKpG+1yDhxnIsYJIxmVTNb787hJOn78hvd27T7mOelMsTOUWr29hdgCXyqqk1QLLMChafcBDpsl3dnKcy4spwFRu9tO/wreJwMqLktIAHGaq4jp8HEqMmiGUgZ0XcOVatUMp1FIQVRZXgLRGzSInXYe2zdLQz5iDm2pWEFmGFKhVXBRH0HAUrzjWrVuHZcuWYfLkyejVqxdOnz6NFStW4KeffsL69eujLV7M426vHz2wrSySyhnt5F4h1p9vwLcTui/AyLPPfflMnArAlx9BwwXvX6iPjyOaUTOEMqgy23ChrMrlmK4xMTm/O04ap2qQY9ShZ16WZGLKMWodq+kwOaejjaIVhyiKWLduHcaOHYvf//73AIDevXvDYDDg8ccfx4kTJ9CxY8coSxke6jKTBGJG4TgWZTfMsDNsTUE/FoIgQBRdD94Oh13VWczP2wTr3r/CUTrdUcKEZRhHCQ+RgYoD7ALwzNReYBiH6em1d0+g5IwJ5dVWaJNUMOiTsOyJATDok2DnRfxxWm/wvAiL1Y5rFRZH61k4FIDTGbx0Vl/YeRGCIELFshB40a+T2P2+lN0wg9VwYHkxeEcmA1nW+fZ//YiSMyaZsuE4tsZMJ9QUb2S9Fm8MlFA8c+d+pnIzeIYBy7I1z6h+MsU7guj4nrhHLV0sdYS4Xq90BX5wLIOsdC1uMurQvV2GzMRU2zmdCCh6xJWVlbjzzjsxYsQI2fbWrVsDAM6cOROXiqMuM0kgZhRXkt0BmdkpScNh274fcO+wDlCr5I7t56b38dv7wXkOU4UZa986DlO5GY+OzceRExfRL78ZFv/1kOxaD93dCQe+PgeeF7Hgz67EvXn3F2DrByVS+9ZHx+bjn//+L+4d1gFQy5fw13zkXzC84FEaxNt9cbaQnT0uX1bZ198qheNYmCptWLfzmKzO1e7PTkrKxltPcvf7O35oh6DMWqF45vLzHPCQPViZ4gmrjcclU7XLrFTmWkFYba77oU1SIaeJFp1bGyXlkGPUoknjwJ3TiUBMOsdXrlyJV155BXv27EGbNm0COiaWnOMix/oo8e3wLbAaDqfP30CyRiW9DZvKzbLIIl/nmD66C2x2Eet2HsP00V3wzLovpc+XzOwDOy/KJth59xfAZuchCJBdy2m+yjSk4OkpvfDMun97vVbzLD3me5GjdoOkKaM6Y93OYwGNwVsElb/9p4zqjO3/+hHjhrZD0ww9ONb/27ev8zw7rTeSapolBXJ/fckZzDWd5wj0Xvi7B8HKFGuIoojyKhsulFaiwirgx5/LJBNT6XUznL9+BoAxLVlSCtlGrWRi0mvVYct9iBTkHPfCN998g7Vr12Lw4MEBKw0APm+AErlsqvJqMgLjeJCnL1yXnMzON8q/7TkBMAwyMvR+z+HesrV2+1FBAF5715F4l5uVijOXKsAAmLvS04nt3haWY323h7Xz3v0Ltdu3SgmGAYzBfZ9A7pteq0bJGROeWfcl1i8YgkyD1uPYQM7DcSzSa44N5P76kjOYazrPEei98HcPgpVJqfC8gItlVfjlUjl+uVxR88/x/xXVrtwHjZpDs8xU3NzaiGaZejTLTEWzzFTclJGKJHVsO6frItzPOKYUx5EjRzBt2jQ0a9YMzz77bFDHxtKKA5z3yCGIIq5eq8Lztcp1rNjqKNcBUXS9afg4h3vL1trtR81WO0zlZjy/6SDmTyrEup3HMGVUZ6/ncbZfzTSkgBe8t2g1W+3gffgXardvdTrLAxmDbJ8A7pu7rD6PDfD+B3N/A7pWoNcM9F74uQdByxRlqi32mnyHyprkOFftJXfndJpOgxyjFj06ZNasHLTIa5sJ0W736py+ca0qksOIOJTH4caePXswb948tGzZEuvWrUNmZmZQx8eS4vBnz66dd+Hk1XmDkMwxkvlFreFQWss/4G6Dv2vAr6BWs1j62mHp87n394DdLuKlN47AoE/GxNs7YtenJ2XFDp3nee3dE3X6OBrpNGAZwGwVsOQ112fefBy7PzuJe4d2QONafprKmsQpZ2HFrHStzwKKvnwcTlmDKSkfkA9J0T4O135K9nGIoghTuUUyKbmimCpxrULunM40pNTkO8hNTNpktcd5EzmPhRRHDRs3bsSSJUtQWFiIVatWQa8PfhkWS4oD8B1B48uG7d6Jz3Esg/JqK1KSVGDg+BKwNf2w7XYB63cdx7VyK8YNbYdsow5qFQurjUd5lRVVZjuSNSoIoiOaqbE+CdpktUsWloHVLjje5lgAgqMkgp0XIYiuaKu1bx/Dl99dkiUOqjgGnIqF1SZAFEVJJkZ09B2vPQnWnpyfnFQoUy7+7luSRgVRFLy2tq3v/a+9jzP50V9L3EAJZVQVo+ZgsfCO+6uAqCqb3emcluc9XCyrgsXmClFISVJJ5TRyjI4M6myjFhmNHdF8gUKKI8EVx7Zt27BgwQLcdtttWLJkCTSa+mVWxpri8EV93kydPpCSMya8WjQIyWoOp85f93CuL53VF1ab4DczO5jJq6FZ18E6x2tDk0fkx15eZZUUgruJ6cr1arjPNMZGya5Vg1EnmZga6UJTmI+efQI7x0tLS/Hcc8+hadOmmDBhAr7//nvZ57m5uUhPT4+SdNGhrmJ33hLXVmx1lPiw2ngwAOy8iC17f5BVtW2fa4C9Jqfh6Sk9ZZ87cx44MAFnUzu76SXVKBCLIAbdB4N6UCgTXhBw9brZ5XdwMzG5O6fVKhbZ6Vq0zNHj13lZkokpK10b987peEfRv7/PPvsM1dXVOHfuHCZMmODx+dKlSzFq1KgoSBZd/LU49TbZGvTJ0CapZWG2Ttt/yRkT2ucaMPH2jlLYrDffgAoOpbR5739kiXGb9/7HUV/Ki5z1MTXJjqceFFHFbLW7OaVdq4dLpirpJQMAGmnVyDbqcEv7DMfKoaZIX3pactxmTic6ijdVhYp4MlX5MwF5M+88PaWn14qyix7qBYvVjlStBmU3zFIl2pIzJmQaUvD8jL4ARKg4Bgwvws4AF65WyRzlj47NR04TLRi7F0XAcZi3ej+cdbBGD2yLtFQNmqSlQFXLn+FrrHWZ5fzdCyWbK8JdQDHQsYuiiGsV1lqRS47/N5VbpP1YhkGGIUUyKWW7ZU6npng6p6ONkp99uEl4UxUhx9dEaqyp8uosW167llOOUSebvJ2rBTAiKs12FLtFQ7n7Q0qvV2Puyv3SdfRajUctqxVbv3LUovKCvaaEibfiiYFEOPkzy8VyEcJoyG6zC7hs8iyrcaGsCha3CsHJGg45Rh06tjA4FES6w7zkLDVDEAApDkXjVATOWk1gGGze+x+PwnvPTuuNFLfw26L7C2TmJIBBz7wsj7Da+ZMKsfuzkx6KwJllfL0mHNJ5neem9/HqcxAEEd4s1myNqclb8cRACwb6MsvFchHCcMpeUe3InP7qVBl+/G+Z5H+4ck3unE5vlIScdC36ds5xRDCla5Ft1IW1axwRP5DiUChS/4oyi8w38fj47rhW7mrXetlUDVO5BVxaijQZXblmluosAcDLj/XHpDs64em1n3tMVlNGdZZasjq3p6VqXNnobtsZxnuiH8vCa9EnFcdg9rh8qDg2pE5ujmNhA/D4+O6yAoSx4jhvqNNfEERcvWF2rRpqOsZdKKuSJVaqOBbZ6SnIzdKjZ8csKcQ1Kz3Fo2oAQQQDfXsUSu3+FYBjcnl581GPOk/XK6ww6JMks5AuRYV59xdi8V8diuRahQWNRO9lQdJS5eHNmYYUpDdKxrqdx2RRVw5ThacZzF+xQIYXYdAnAQidk9tfuLGjX4fyHeeBOv0tVl4W1uo0MV0sq4bdzaSl16qRk65FftsMKQcir20mGDsv5ckQRCghxaFQeEHev8KJ+2SfaUjB3IkF2P/1L2jTNE0yRy3f8hUM+mT8fkJ3GNNSIDqsXOiZlyVbXWQaUtBI5+ot7oym2vpBCe7s3wanz9+QKQimjpLmHmPgBejUnFe/S317dPsKN54+ugsM+uSw9v0OFbV7jRjTkjFmUFt8cvgszl2tlFYPZTdczmmGATIaO5zTnVoZZd3jvDmnM4y6hHUOE+GHFIdC4VgGZqvd65upMS0ZS2b2xfUKK/6xrwTjhnZAkprB5Ds7SeXLDfpk2OyiLMS2aFIhAEilPuZPKkRKEoviGX0dfgqWAcsBvxvcDho1i8Uz+kq9JtwVhK9QYG/wvADwCErh+D2fDzNP0ww9kljl9puw845AAUdynGPVoEtRI7nKitLrZqx681sAQJKGQ066Fu2bN0a2W2JcpkELtYqc04QyIMWhUFQAstK1Hn0knnygEH/ZcUy2cpDaucJljvLmkC7edBBPT+mFe37T1hUSa3UkBXIAwAMC77i2UBNpE6iCqAt/uSfB4NvMowylUWm2eZTVuFBWhSumaghu3mmDPgk5Ri365OXIVg9KcU7Hcr91IvyQ4lAoTjOPNkOH52f0gSAAKpaByIgypQG4HKvuk6pURrvWfjcqLShafQBriwaBCSCFR2kTiK+WspE0UQmiiLLrZpx3c0o7HdQ3ZM5pBlkGLZpl6FDQIQM56Y6e00rvGhfLoc5EZFDut5eQzDwsHP/Aw2fZbOek7pxUffX0dm4PxImsxAmkrpIrocRSU5nXvd+0sw6TzS3hUZesQk4THbr+qokjKa5mBdEkLTa7xsVyqDMRGShzPEBC8eYdigKBgWZTgwHKKxtWXjuQToOhIhwrm0AyaEVRxI1Kq2RScjcxld4wS/sxAJo0TpaypW9qoqsp8a2FXlu/wpvhpCHZw3aG8VvoMhagzHHKHI86oXjzbkg/Bff96nrjdvoSAIdD+sXZ/WXltafe1TmgSZnjWJjKrV47DYY6VyISKxs7L+DKtVplvWtWENUWV0MrjZpFTroObZuloZ8xR6rcmpWeArUqMQrzUY0woi5oxREADS3vHcw5QnEtd+r79uGvp3Zulj6kK45QjrnKbJMqtV6vtuPkWRMullVJfiAnjVM1LrOSW3OgxvqkuCjM15C3TiWaKIOFVhy04og6oSjvHeg5lFJK3JccNzVJDbkjOtgxC6KIshtmWdSSM4v6eqVn17gcow7d22XIuscp2TkdbSLpRyJiE/r1BEAolu6BnkMpZgJfcqg5Fjwf2vglX9fieQEXrla6MqdrTEwXy6pgdXNOa5NUyGmiRefWRlnl1o6/yoCprDKksiYKoQqfJuITMlUFgJJ8HMFS32VrpMwVoiiiysLjh3PXsend71FeZYNGxUJfU+rd+cQYAMa0ZI9+0zlGHfRatdfcBzJXJObYgcQeP7WODSHxElUVLA21dYdKDl4QcOWauVZinOP/K80u57RaxSLbqMVNRlfUUnZ6/brG0eSRmGMHEnv85ONQEKFYugd6DqWYCeojR7XFLi/MV2Niqu2cTtNpkGPUoqBjlqw5UHoj6hpHEEqHFAcRNKIowlRukZSCM4rpQmklrlW4nNMs43ROa9GtbRPHKqLGxKRNVl7XOIIgAoMUB+ETm53HpbJqj8S4i2VVsNhc64+UJJWjlHfLdMkxnWPUIqMxdY0jiHiEFAeB8iqra/VQoxgulFbi6jWXcxoAjI2SkWPUom1zV2JcjlGLRjplFOYjCCIykOJIEHhBwNXr5ppifHITU0W1qzCfWsUiy6BFy+xG6JWXLa0esgxaJGkSI3OaIAj/kOKIM5zO6Ys1UUtlFVb8fP4GLpmqYHfLA2mkVSPbqMMt7TOkftM5Ri2MjZKpaxxBEH4hxRGDiKKIaxVWWWKc08RkKnd1jWMZBjlNHL6Gzm2MUs+H7HSt165xBEEQgUCKQ8HY7AIumzzLalwoq4LF6nJOJ2s45Bi16JBrkHpO5xh1joim7LSEjWcnCCI8kOJQABXVNteqwc3/cOVaNdzTM9MbJSEnXYu+nXMcyqHGxKSUrnEEQSQGpDgihCCIuHrD7Fo1uCXIuTunVRyL7PQU5Gbp0bNjlrR6yEpPQbKGHhdBENGHZqIQY7baHbkPbmali6WVuFhWDbtbuY7UFDVyjFp0b9cE2ek6ycTUJC2FnNMEQSiamFAc77zzDtasWYOzZ8+iadOmePjhh3HXXXdFTR6nc7p2v+kLZVUou+FyTjMMkNE4BTnpWnRqZZRaimanK7NrHEEQRCAoXnG89957mDNnDiZOnIh+/fph3759mDt3LpKTkzF8+PCIynKprArr3v0e565UwuzmnE5Sc8g2atGueWNZYlymQQu1ijKnCYKILxSvOP70pz9hxIgRmD9/PgCgX79+uH79OpYvXx5xxQEAaboktMjSy7rHGfRJ5JwmCCJhULTiOHv2LM6cOYMnnnhCtn3YsGF47733cPbsWTRv3jxi8mSlazHzns4Rux5BEIQSUbTiOHXqFACgVatWsu0tWrQAAJw+fTpgxZHIDmcae2KSyGMHEnv8oRi7v3MoWnGUlzsS11JT5c1EdDodAKCioiLgcxkMutAJFmP4asaSCNDYE5dEHn+4x65oz62zOWFt/4FzO8sqWnyCIIi4RNEzr16vB+C5sqisrJR9ThAEQUQORSsOp2/jzJkzsu0///yz7HOCIAgicihacbRo0QLNmjXDP//5T9n2vXv3omXLlrjpppuiJBlBEETiomjnOAA88sgjKCoqQlpaGm699Vb861//wnvvvYeXX3452qIRBEEkJIwoutdfVSZbtmzBhg0bcOHCBTRv3hxTp06NaskRgiCIRCYmFAdBEAShHBTt4yAIgiCUBykOgiAIIijiWnG88847uP3229GlSxeMGDECO3bsiLZIYefEiRPIy8vDxYsXZdv379+P0aNHo2vXrhg4cCA2bNgQJQlDiyAI2Lx5M0aOHIn8/HwMHjwYxcXFstyfY8eO4b777kN+fj769u2LP/3pT7DZbH7OGhuIoohNmzZh2LBh6NKlC+68807s3r1btk+8PvfazJw5E0OGDJFti9ex2+12dOnSBe3bt5f9y8/Pl/YJ99gVH1VVX5RUjj1SnDp1Cg8//DDsdrts+9GjRzFt2jSMGDECs2fPxpEjR7B06VKIoojJkydHSdrQsG7dOixbtgyTJ09Gr169cPr0aaxYsQI//fQT1q9fj59//hmTJk1Cfn4+li1bhpMnT+Lll19GRUUFFi5cGG3xG8Srr76KFStWYNasWejWrRs+/fRTzJkzBxzH4bbbbovr5+7Ozp078cEHHyA3N1faFs9jP336NCwWC5YsWYKWLVtK252VNCIydjFOGTx4sPjYY4/Jts2ePVscPnx4lCQKHzabTXz99dfF/Px8sbCwUGzXrp144cIF6fP7779fHDNmjOyYpUuXij169BAtFkukxQ0ZgiCIBQUF4qJFi2Tb3333XbFdu3bi999/L86fP18cMGCAbJxvvPGG2LFjR/HixYuRFjlkWK1WsaCgQPy///s/2fb/+Z//EcePHy+KYvw+d3cuXrwoFhQUiP379xcHDx4sbY/nse/atUvs0KGDWFVV5fXzSIw9Lk1VznLsQ4cOlW0fNmwYTp06hbNnz0ZJsvBw5MgRvPjii3jwwQcxZ84c2WcWiwWHDx/2ei9u3LiBo0ePRlLUkFJZWYk777wTd9xxh2x769atATgqDhw4cAC/+c1voNG4Oi4OHz4cPM9j//79EZU3lHAch7/97W+YOnWqbLtarYbFYonr5+7OggUL0KdPH/Tq1UvaFu9jP3HiBHJzc5GSkuLxWaTGHpeKI5By7PFEmzZtsG/fPsycORMcx8k+O3v2LGw2W1zei9TUVCxYsAC33HKLbPu+ffsAOO7LhQsXPMaenp6O1NTUmB47y7Jo3749srKyIIoirl69irVr1+Lzzz/H2LFj4/q5O9m2bRu+++47PPXUU7Lt8T72kpISaDQaTJ48Gfn5+SgoKMDChQtRUVERsbHHpY8jlOXYY4EmTZr4/CzR7sU333yDtWvXYvDgwWjUqBEAz7EDjvHHy9j37t2LRx99FABw66234s4778SJEycAxO9zP3fuHIqLi1FcXIz09HTZZ/H+nf/Pf/6DiooKjBkzBtOmTcPx48fxyiuv4PTp01LTu3CPPS4Vh0jl2CV83Qsn8XQvjhw5gmnTpqFZs2Z49tlnYbVaAXgfuyiKcTP2m2++Ga+//jpKSkqwfPlyTJ06FY899hiA+Hzuoihi/vz5GDBgAIYNG+b1cyA+xw4AL7/8MtLS0tC+fXsAQEFBAYxGI/7whz/gwIEDAMI/9rhUHFSO3YWve+H8O17uxZ49ezBv3jy0bNkS69atg8FgkJ63t7esqqqquBl78+bN0bx5cxQUFCA1NRVz586VJs94fO5vvPEGSkpKsHv3bimC0Dleu90e99/5wsJCj2233nqr7O9wjz22Va8PqBy7i9zcXHAc53EvnH/Hw73YuHEjnnjiCXTr1g1vvPEGMjMzATiW51lZWdJzd1JaWoqKioqYHvu1a9ewY8cOXLp0Sbb95ptvBgD88ssvcfvc33//fZhMJvTt2xd5eXnIy8vDjh07cObMGeTl5eHw4cNxO/bS0lJs27bNI8DHbDYDAIxGY0TGHpeKg8qxu0hKSkKPHj2wd+9e6a0McPz49Ho9OnXqFEXpGs62bduwePFijBgxAuvWrfN4o+rTpw8++ugjyWwFOMbOcZzXN7dYQRAEzJs3D1u3bpVtd5oqOnfuHLfP/ZlnnsGbb74p+/eb3/wG2dnZePPNNzF8+PC4HTvDMFi4cCFef/112fY9e/aA4zj07t07ImPnFi1atCgkZ1IYer0ea9asgclkAsMw2LhxI95++208/fTTaNu2bbTFCxsnTpzAhx9+iAceeEBykGVnZ+PPf/4zTp48iZSUFOzYsQN/+ctfMGvWLPTs2TPKEtef0tJSTJkyBVlZWfj973+P0tJSXLx4Ufqn0Whw8803Y8OGDTh8+DDS0tLw8ccf44UXXsCYMWMwcuTIaA+h3qSkpKCsrAyvvfYaVCoVrFYrdu7ciZUrV+Kee+7B6NGj4/a5GwwGZGVlyf7t378fly9fxpw5c5CSkhK3Y09JScG1a9fwxhtvQBAECIKAnTt3YsWKFbj33nsxcuTIyIw9JNkgCmXz5s3ikCFDxE6dOokjRowQ33777WiLFHa2b9/ukQAoiqK4d+9e8Y477hDz8vLEgQMHZ5wk1QAABalJREFUiuvXr4+ShKHj7bffFtu1a+fz344dO0RRFMVDhw6JY8aMETt16iT269dPfOmll0Sr1Rpl6RuO1WoV165dKw4dOlTs1KmTOHjwYPHVV18VeZ6X9onH5+6NuXPnyhIARTF+x+587sOGDRM7deokDho0KOLPncqqEwRBEEERlz4OgiAIInyQ4iAIgiCCghQHQRAEERSkOAiCIIigIMVBEARBBAUpDoIgCCIoSHEQCU9paSmqqqqCPq6iogJlZWVBHzdv3jypQF0wvPLKK2jfvj1++eUXv/u99dZbaN++Pb788suA/iaIYCHFQSQ0n3zyCYYPHx60Ajh+/DhGjBiBH3/8MUyS1Z+CggIsXboUbdq0ibYoRJwSl9VxCSJQvv32W9y4cSPo43744Qdcvnw5DBI1HGe1XIIIF7TiIAiCIIKCFAeRsMybNw8rV64EAAwaNAj33XcfAEdrzhkzZqBHjx7o0qULfve730ntaAGHr6GoqAgAMHHiRAwcOFD67N///jemTJmCnj17Ii8vD/369cPChQvrtarxxalTpzBx4kR06dIFt956K5YvXw6bzSZ9Tj4MItyQqYpIWMaOHYuKigp88MEHKCoqQtu2bfHtt99i4sSJSE1NxQMPPACdToedO3fikUcewcKFCzFhwgQMGTIEV65cwdatWzFt2jR07twZALB//3489NBD6N69Ox599FEwDIMDBw5g69atsNlsKC4uDoncs2fPRs+ePTF37lwcPHgQq1evxoULF7B48eKQnJ8g6oIUB5Gw5Ofno3379vjggw8wePBgNGvWDL/73e/AMAzefPNNZGdnAwDGjx+P8ePHY+nSpRgxYgQ6dOiAbt26YevWrejdu7dUqnrTpk3IycnBxo0bodFoAAD33nsvxo4di/fffz9kimPAgAFYtmwZAGDChAkoKirCW2+9hQceeKBe0VoEESxkqiKIGq5evYpvvvkGo0aNkpQG4GiGNXnyZJjNZnz++ec+j3/11Vexfft2SWkAgMlkQmpqar3CfX0xefJk2d9OE9snn3wSsmsQhD9oxUEQNZw7dw6A9/aaztDW8+fP+zye4zicPXsWy5cvx08//YQzZ854tHYNBa1bt5b9nZubCwB15ncQRKigFQdB1OCvNY0gCAAAtVrtc58tW7ZgzJgx+OKLL9CyZUtMmTIF//jHP0LeaZBhGNnfTrk5jgvpdQjCF7TiIIgamjZtCsARtVSb06dPA4DMhOWOxWLB4sWL0bNnT2zYsAEqleuntXz58pDKee7cOVn7Y6dszpUHQYQbWnEQCQ3LOn4CoigiIyMDnTp1wq5du3Dx4kVpH6vVKjm8+/TpIzvOuRIxm82orq5Gy5YtZUrjxIkTOHjwIADAbreHROZ//OMfsr83btwIhmFkYcEEEU5oxUEkNOnp6QCAdevWoX///liwYAHuv/9+/Pa3v8X48eOh0+mwa9cufPfdd1iwYAEaNWokO27z5s24evUqRo4cia5du+Ktt95CamoqWrVqhR9//BHbtm2TlExlZSXS0tIaLPPu3btRUVGBLl264JNPPsFHH32EKVOmoEWLFg0+N0EEAikOIqG5/fbbsXfvXrz11ls4ePAg3nvvPWzevBkrVqzAhg0bIAgCOnTogFWrVmHw4MHScb169cKIESPw0Ucf4YsvvsDQoUOxfPlyFBcXY/v27bBarWjatCmmTp2KNm3aYNasWfjiiy8wbNiwBsv8l7/8Bc8++yzeeecdZGVloaioCJMmTWrweQkiUBjRn0eQIAiCIGpBPg6CIAgiKMhURRBR5MqVKwHtp9VqodPpwiwNQQQGmaoIIooEWiJk5syZmDVrVpilIYjAIMVBEFHEXwkTd6jHBqEkSHEQBEEQQUHOcYIgCCIoSHEQBEEQQUGKgyAIgggKUhwEQRBEUJDiIAiCIILi/wFlbKvTBJVDDQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(data['total_bill'], data['total_bill'] * 0.05)\n",
    "ax = sns.scatterplot(data['total_bill'], data['tip'])\n",
    "ax.set_ylim([0, 11])\n",
    "ax.set_xlim([0, 53])\n",
    "fig = ax.get_figure()\n",
    "fig.savefig('5_percent.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(data['total_bill'], data['total_bill'] * 0.25)\n",
    "ax = sns.scatterplot(data['total_bill'], data['tip'])\n",
    "ax.set_ylim([0, 11])\n",
    "ax.set_xlim([0, 53])\n",
    "fig = ax.get_figure()\n",
    "fig.savefig('25_percent.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(data['total_bill'], data['total_bill'] * 0.15)\n",
    "ax = sns.scatterplot(data['total_bill'], data['tip'])\n",
    "ax.set_ylim([0, 11])\n",
    "ax.set_xlim([0, 53])\n",
    "fig = ax.get_figure()\n",
    "fig.savefig('15_percent.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(data['total_bill'], data['total_bill'] * 0.1)\n",
    "ax = sns.scatterplot(data['total_bill'], data['tip'])\n",
    "ax.set_ylim([0, 11])\n",
    "ax.set_xlim([0, 53])\n",
    "fig = ax.get_figure()\n",
    "fig.savefig('10_percent.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d302394448>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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T2FzbgD2H2xDqt1lakIWaylLUTC5BUV56ZbiISnD8+c9/xsyZM/HKK6/oDNMTJ07EvHnzcMMNN+D555+PueAgiHgTqf0imewD67YchiQxiIKm/qBgvsFBVlR8s78Zm3Y24Kt9zZCVrqSCOVkGzJhcglmVpRhVkp22DjxRCY5jx47hxz/+cdiXIYoiLr74Yjz66KMx6xxBJIp42y9iQVO7G7k2I2Sla92bTLXKUxnOOeqPdWDTTi2poMMtB88ZJQFTxhejpqIUFWPyg4I7nYlKcJSXl2P79u295on69ttvKa6CSAtSMb6hKNcMu9unm7iSXdglO40tzqDd4kSbK3icMWDyqHzMrCjF1PHFsJiS2kE15kQ12oceegg333wzli5diltuuSXo1eRyufDaa6/hnXfewYoVKwalowQRT5LNfhEJC6rL8OZH+yAzJWWEXTLS4fTii7oT2FTbgP3HOnTnRg6xocafVDA/O7ZepKkE46GuUf0wb948tLW1oaOjA4wx5ObmwmAwoLm5GZxzcM57qLEYY9i1a1fMOx4tlHIkM8j08R9qcma0V9VAP3+vT8FX+5qwaWcDdh5o0SUVzM82YWZFCWoqSjGiOHlz3iVtypGpU6emrbGHINKBaZNKgnmriL5ROceeQ63YVNuIrXtOwO3tCs6zmEScNX4IaipLMaEsL6WC8+JBVIIjmmy0BEEQyciRk3Zs2tmAzbsa0drpCR4XBYbKMQWoqSzFmeOKYAxxjCD0ZJZFhyCImJMKFQRbOz3YsqsRm2ob8N0JfXbZscNytKSCk4YgOys5kwomG30KjkmTJmHZsmVYuHAhAC1eoz9VVbLYNFKJVPjhEQMjHp9taBtDi22YPWVY3L4/O+qbsOK9Ori9ChSVo8PhxYr36rD4kkkJ/w67PDK27z2JTbUNqDvYqgvOK84zo6aiFDUVpSgpINVetPQpOC6//HKUlXV5ZMQ6nQhBpTvTmXh8tt3baO1wxfX7s/qTfXC4ZTAGCEyzGzjcMlZ/si8h319FUbGjXquc9+Xek/DKXcF5VrOEGZM1I3f5sByy154CfQqOJUuW6P4+evQofvazn6Gmpibs9R9//DEee+yx2PUuA6DSnelLPD7bdVsOQ1Y4Op0eyIoKgyTCbBTj9v1pbHX7hYY2CTMAKjgaW+MXdMg5x8GGTmyqbcDW3SfRZu+yW0iigDNPK0JNRQlOH1sISUz/4Lx40KfgcLvdwfKtAPD5559j7ty5GDVqVI9rVVXFP//5Txw5ciT2vUxj4p2aO5OIRE0Ua1VS6PPa7R7kZZuAECNr6Gcbi7aPNTngcPvAmACBMciKig6HDCUkDUakbQ2sP1yrK+HfbSiq9jcDx476pkEVXifbXNhc24BNtY1oaHEGjzMAE8ryUFNRirMmDMG+o21Yt+Uw3vjw24jGlQyq42ToQ1/0KTicTicuv/xydHZqvsGMMfzhD3/AH/7wh7DXc85x9tlnx76XaUwqprZIBSJRE8ValdT9eR0OL1o63GCMBSOLA59trNrW0oswBEpQC4xBBdOlHRnMd1FSkIXjzQ4oKnSxD6LIBkVlZnf5sHW3Fpz37ZF23bnhRVbMqR6FyrI8FPp/P9GOKxlUx8nQh/7oU3AUFBTg0UcfxTfffAPOOZ577jnMnTsXEyZM6HGtIAgoKCjAJZdcMmidTUdSMbVFKhCJmijWqqTuz8u1GdHS4UFbpwdmo6j7bGPVtigyQNZW+wwIrv5FsUt/P5jv4qrzy7Fi7W50htScEAQtaE4UhZiozHyyih31TdhU24gd9U06oZhrNaLan1Rw5BAbhgzJ0QXBRTuuZFAdJ0Mf+qNfd9zzzjsP5513HgAtyeGPfvQjnHHGGYPesUwhFVNbpAKRqABjrSbs/rwsswGcc7TbfXC6Zd1n+9oHe2PS9vAiKxpanHB5FciyCqOBwWSQUBriKTSY76KqvAiLL56I597eCZVzSJKAnCxDcOwDfZcq59h3pN1vtzihSypoMoiYOr4YNZUlmDyqAILQu5E72nElg+o4GfrQH1HFcXQ3lhOxIZlSc6cLkagAY60mDPc8SRJRPtyCe66bGnX/IiGwYzWbJBglASrn8HgV3Y51sN9FVXkRyofnxGQ8x5sdwaSCoRMlY0DFmALUVJRi6mnFMBkjC86LdlzJoDpOhj70B7kYEGnJguoyKIoKj08B5xwen9JDBRjJNbFuM9ZtV5UXYdHc8cizGuF0y8jPsWDR3PG6hUg83sWp3N/u8GL9F9/hP1/9Av/ff2/B/9t4KCg0RpVk40ezT8Pjt5+NX//wTNRUlEYsNAbSr1h/JwZCMvShPyhynEhLIlEBxlpNGM3zYtl26I41XKK7eLyLaO/3eBV8+e1JbKptRO2BFqghuVYLc8yoqSzBzMmlGFZkjfAtaEblj1bvwPGT9h7tR9qvZFAdJ0Mf+iOq7LipDGXHzQwSPf5Eu1EmevyhdH8X82aMhEEUsam2Adv2noQnJKlglknC9ElDUFNRinEjcqNOKhjwRDIZRQiMBR0Ruu++0pmkzY5LEETvpIIbZbwIvAtBYJBEhsMn7Hj2r98gdO0mCgxV5YWYVVmKqvJCGKSBJxUMeCKZjRJ8spqUnkjpBAkOgogRqeBGGS/e/ewgXF4FHq8Cn6wPRjxtRC5qKkoxbeIQ2CyGmLSXCp5I6QQJDoKIEZk+eTndMrbt0YLz6rtVzpNEBqvZAEEA7v/xWTFvO+CJZExiT6R0ggQHQcSIVHCjBGJrh5EVFTv3t2BTbQO+2tek210IDLBaDLCaDTAatODWPOvgpC0PuCW7vbLOxpFMnkjpBAkOgogRqZAFIBZ2GM459h/rwKbaBnxedwJ2ly94ziAJmHJaEYYWZuGzb45DksS4vItA3z/68lhYryoitpDgIIgYkQpulKdih2lsdWJzrVYM6USrK3icAZg4Kh+zKksxdXxxMC/XmKE5cX0XVeVFmD1zTNJ4laUzJDgIIoYkexaAaO0wdpcPn9c1YtPOnnaLkUNsmFmhxVvkZ5t63Jvs74IYOCQ4CGIQSHQ8R29EYofxyQq+2teMTTsb8M3+Zl3W2/xsk5ZUsKIUI4aE9/En0h8SHETcSJbJdLD6EXjusSYHXF4FVrOEHKsxqeI5erPDzJ8xEnsOt2LjzgZs3XMCLk9XcJ7ZKOKsCcWYVVGKCWX5fSYVJDIDEhxEXEiW4LjB6kfocz0+BarK0enywSAJyDIbkiaeo7sdJttiQGGxFf/7wV60dHRVzhMYQ+XYAsyqLMUZ44p0OxSCIMFBxIXBDI4L3UEMLbZh9pRhvT5zsPoR+lxF5RAFBpVzdDh9yDIbBjWeI5rxA0BZSTaqyouwubYBBxo6caChy5g8ZmgOZlWWYvqkIcjJGhzXWSL1IcFBxIXBCo7rvoNo7XD1uYMYrH6EPlcSBciKVlhJ9sc1DFY8R6Tjd3tlbN+rJRXcdbAFoRnqivPMqKkoxcyKUl0dD4LojZQTHHfccQf27NmD9evXJ7orRBREExwXjQ2i+w7CbBAhKzy4g+j+LLM/EC3WQXqh48uxGtHS4YbKNSEymGmx+xp/xZgC7DrYik21Ddi+9yS8vq7gPKtZwoxJJaipLEX5sBywKJMKEplNSgmOd955B+vXr0dZWfIEVBGREWlwXLQ2iHA7CEVRUX+0HXc+/a8eRmqnW0ZguR3LwLTQ8ZmNIrKzjLA7fTAaBORZjYPmCNB9/JxzgHMcbOjEXc9tREdISVdJFHDmuELMrNCSCkoileMhBkbKCI7Gxkb8/ve/R2lpaaK7klR0X1FfM28iRhUNvrohWs+kwLnVn+zD8SanVmZUZHj5vToML7IG7w9dQTvdPnQ4ffDJKp7/204MybfA7VV07XXfyTjcMlo6NLVTp8sHzoE2uxeqypGfo+0qJIHBZjH02feBji9wT0m+BeedMRS7D7ehqd2NdVsO664LbWf1J/vQ2OoGwFFSkIWrzi+PWMgExi8yBofbB4dbDqb9cPvTlo8fmYeaihJMnzgEWebYJBUcTJLF+47onZSpx/HTn/4UNpsNJpMJ27Zti1pVlY71OEJX54HVMzjwo9njBvWHFq7dSGofBO6TFY4OhwcAAxiQbTHAIAlYNHd8sBa3yyOjpdMDBkBVOVQOiAJQkGOGKArB9gDo+tLY4oLXp4AJgKpPyoriPDMsJglOt4xlP5sV8/FF+4wd9U1Y8V4dHG4ZjAU2QhxWixGLL57Yb1sOtw9//9d+/POrY/Ap+u92QbYJ508ZjpkVJSjKtUTU52TgVN99MtUjiTfxrMeREnvVt956C7W1tfjtb3+b6K4kFaGrc8YYTAYRksSCq9t4tiuKQr/tBu5zeWQwJkAUGBgAl1cJ3l+Ua4ZXVtHh9IFBcwsNLG0YE9Dp9Ona6146NbCTERhDQG0f0N53OH3odPrgdMu454WNWPb6duyob4rZ+KJ9xroth+H2KmBMG6coMDAmwO2Re23LJ6vYvvcknnv7G/zqmQ34aNvRoNBgDCjMNeO6OePw6L/PwvdnjU4poQHE5t0Tg0/Sq6qOHj2KJUuWYMmSJSgoKBjwc3qTnKlMi92LbIukM2xKnKHV7kVxcXZ82xX7bzdwX1ObG5p6nUGAZpOwmiW02r247YoqvPj2DsiyClEAOLR/ksggCoCscBgkQdfe7OJszJ45BgDwwAufYdf+Zm0SFhl8sorAWtznU9Ahq8jLNiLXZoTd7cObH+1Dbm4Wpk0qOeXxRfuOWuxeqJz7hZx2ncg4ZIXrruOco+5gCz7ZdgQbvjqqSypoMoqoqRyKC84aiTNOK4KY4naLWLz7wfzuJzvxGntSCw7OOR544AGcd955mD9//ik9Kx1VVQU2Yw9PJUVVkW8zDup2PVy7Hp/Sb7uB+ySRQVY4BMahcg5RFOBwy8i3GTGqKAs/mj0Oy9fsgscnwyAJgCSAcw5F1SYRn6z22t4V54/D7oMtwVgKUWDa584AgCE7ywCbxQhZ4RAFATJTsOqD3Tq70EDHF+07KrAZ0dbh1oSH/xpNJceQbzPimz1ajqhNtQ06d2HGgMmjCzCrohRTxhfBbNR+xi0tjpRX1Zzqu0/18Z8KpKrys3LlSuzZswcPPPAAZFmGLMsImGRC/z9TWVBdBkXRJlHOOTw+BbLMBz2Nd7h2I/FMCtxnMUngXIWicnAAFqOou7+qvAi3XDoZRoMIj0+rICcrHLKiIjvL0Gd70yaV4JKZZRAYg6KqkESGvGwTinLNsFo076pQwsVwDHR80T5jQXUZzEYRnAMq51BUDlVVIQgMrXYPHli+Ge9uPBjsX1mJDT+6cBweu/1s3HXNmaipLA0KjXQhFu+eGHyS+lv3/vvvo7W1Feecc06PcxUVFViyZAmuuOKKBPQsOQiXxjseXlUDSR8e8JRxexUoCvevKBlEkaG0IKvH/QePd8DtVdB9beBw+VBWkt1ne5eeMxajw6T0XrflcESxJKcyvtDrF80d3+czqsqLsPiSSfjLx9+isUXbeXBo3lDuFi1teUGOSQvOm1yC4cXpp27tTiqkpieS3Ktq//79cDgcumPPPfcc6urq8Oyzz2LEiBHIz8+P6FnpqKoKRzJu1QfiKXPHE/+Ex6dADEmop6iawHn2V+f22lZf44+Ft1SsnquqHHWHW7F5ZwO27j0Jj7crqaDFJGH6xCGoqSjBaSPzIEQRnBfPzz8Z3WaT8fsfL+KpqkrqHcfYsWN7HMvLy4PRaMTpp5+egB4RA2Eg+aHcXlknNACtFKnbKw+4H4O1mo1mfN+dsGNTbQO27GpEa2dXUkFRYKgqL0RNRSnOGFcIg5TcSQWTJWklkRiSWnAQ6cFA8kOZjZK24wiRHSrHKev0T7W4UOgq22wUAc5xrNkJgyQg12YKVr8LHV9Lhxtb/MWQjpzU76DHDc/VgvMmlcBmSf7gvACDmbSSSH5STnAsXbo00V0goiSaPFUB5k0fgTUbD0JRtZ2GygEOjnnTR8Sjy2EJXWUzBhxvdgDQPLdkhaOlw42CHC3I0O1VIIkMj77xJXYfakWokrQk3+JPKliCIfmpmVSwqd0NxoDGTg9kRYUkCsjOMgxaBmAiuUg5wUGkHr3lqZpYlodlr2/H0SYHPF4FisohMKCkIE3K5VUAACAASURBVAvTJhSjINuM5nY3FP99F88chUvP6VJfhtOxz+7mx76jvgmrP61HY4sTAENOlgSL2dAjdUkk+vrQVXZjpweMCdDEGQCm2S1aOtyQRCGY7qPBb+S2WQyonlSCmZUlGDs09ZMKmo0ijjc7wJgAgXUJzqGF1kR3LaEko91nMCDBQfRJLH4I4WwLE8vy8NnOBvhkFXZ/TikA4Aw4etKBo00O5NlMGFliCwqa0UNzdP0Kp2PPzc0KepXtqG/CirW74XB5oQVyqGju9IJ1elGUZw7ec/B4Bz7eflTz+FI5OhxerHivDosvmaQba6jKTVbUYGwJ0LUrUhUOWdGEhkESMOW0IsycXIrKsQXplVSQc2jvlId4vgXzpmQkmWT3IcFB9EosfwihtoUd9U1YvmYX3H5f/dC5JvC/nAMuj4wcqzGs/rw3Hfvbn+7Dr66qCl7j9qc3ERh0+Zw6nT6UFGTBA+D/thzW6mewgADgcLhlrP5kn26cOpVbiNAANKERYNKofNRUlOKsCcVBm0foO02HFanbpyI/24hOlwxZViFJArItEtw+tf+b05RMsvuQ4MhAIp28BuOHEBBGHp8MkTGEzjMM+gWrHDIzdzem92ZwP9HiDLZTf7QdPr9AgNCV84qHPNsoCfD41GB+q0A/VHB/xtouzjtzGFau34tmnwo5zPzImGa/+M21U/ocezqsSANCtLSgK6DS41OQZ83cqoGDVSQsGUmjvTMRCYHJq83h1U1e4ZL9NbW7YZT0X5FT/SEEhJFBEsHRlYgQ0CZ0xrqSEoaqdrob0wPJEEPxyiqGFGQFxxiwI3COYEU+QHt+4NleWe0hsICuTLU+WcHW3Sfwu//ZihfX7ILd1ZW2HNB2KKKg6fyLcs2Qld5VNemUwI8ivHvS23dyMCo/JhoSHBlGNJPXYPwQAsJIS/3RNZkH4V3qKp+iwun29ZquI9zEdcX544JjzLUZIQi6RwcJTV1SkGMCwIPqJkXl4JzDaBBx5zOf4fm/78T+Yx0ANMFmNokQBYY8mxEjS7IxYkg2SgqyIIpCn+9mMARxouielTjPajzlQMpUJ5OEKamqMoxottPRVO2LVG9vNghoaHZqHlSClvGWK5pnUsDALIkMFpMIl0fByTY3RIFhaIE+PXhvwXwAUH+0Q0uvLgmwmQ1weZXgLqEw2xj0qgpU5gOAFWt3w+X2wSt3iReHuyvY0GQQkJ1lhMUsQWAM7XYPHC4ZZpMUcSXBgbglJzOnGhOTbmRSuhQSHBlGNJNXJD+EaPT2O+qb0OGSoagqABY0jGdnGbD4kkm6XFJOtw9Oj5ZyRBIZZI4ezw1MXAHB9fJ7dXB7FQQSqSuKCoeioiDbBFHUSrjec91UXZ/a7B58vqsRZoOoK7MKaF5RJoMADqAwx6xzoc2xGqGoHHlWY8STRKSCOB6ki5E+2cgUYUqCI8OIdvLq74fQlwE9cD4wOdldPmSZJZiN2iQtKypEgSHHakRVeVGw+h+ArkJOAgvmqApnmA8VXC63DDnEvUlg2v3tdi9ybV27C7dXxpd7m7CptgG1B1t09g3RX1bW6q9K6PEp6LB74ZXVHsJ2eJG1hyDqi1BBfLixE26vCpVzLF+zC/Omj9DFqAwm6WSkJxIDCY4MI9bb6d5UX0ebHD0mpxMtThTmmpFlNgTdVDnncPpVQoHdkKKowaR/DJrKKfDc7iq1gOBSFFUnNAB/tLnCwUTg2tmnQRAY/vvdWmzf2wSPryupoNUsYfqkEny59yRyrAYIIYYRo79olKKoMdkpVJUX4eDxDuw90gbGGAwCg8enYM3GgwBwSsJjR30TPlq9A8dP2gfsLRc4TzsRoi9IcGQgp7Kd7q7iMBuEsKtxReE9JidJFNBu9yLLrOVkcnlktHV6wDmw7PXtmFiWh4+3H9VqcKOr+p+icrg8MgSB9VCpBQRXoz9hYECZxKF5OzHGYMsy4s/r9qA9RBUliQxnlBdhZkUpqsoLYZAENDQ7NFVZiP3aK6sYVmQNpmWPxYT6wRdHwPypSgBAZICiascHKjgCuwiTUex3FxGNsKedCBEOEhxExOyob8IKvx0hEGEtiiwYDOeTVV3wsNMTPpNtu90Dg3/3wP3F+b490oZvj7Rrdg/oPaBUleNEq5a6o8PuwbLXtwdX+51Or24XEnqfFqrBdVloGYBcmxE/mj0OMyaV6vq1oLoMK9buRku7G4qqQhQEmE0SfnThuJjqriPJ/BvOBgH0vhsI7CLMRgk+vyDvLeamNztXOGGfiAC27mOfWJaH3YfbTqk2Cgm+2EKCg4iY1Z/s03YDIRHWslcF54Dgrw+O3sMYAGjurA6XrKXsgPYcoGuSB7SdQm/hEC6vgsZWF1as3Q2frPRwF+6LgM2j0+nD6+u/hdko9ZxQggYP1u3v2NFf5t9wNogVa3cDnCPLYgi7G4iFt5wksoS7C3cfe0OLE3uPtCHXakJ2lqHfXdDWukbaNcUBiuMgIqax1e0XGgyMaZHWqj/uQpJESKI+oC8ckiigMM/s/38GSRR6yBq1L1ngT0Xi9shweRQwxnrGgvhhTGsD6Ar60/quVdnrHruybsthZFkMGFpkxYghNgwtsiLLYtBdt6O+Ccte3457XtiIZa9vDxs42R/zpo8ABw/Gi2gldLsy/4aLtXF7ZLi9Sq/xN9HE3PQWgzGsyJrwALbuY3d5FTAwuDxyREGTb3+6L22CLJMZ2nEQUcC7ctt1Q5ZVCBHkuFNVDqOkCYvAs3pEbffZA8AnK0Hh0ltVR5NBq4/R0uHu8UwGzW7S1O7WqTU07yuDToUTuuKOlTdSwI7xwRdH4PbKMBslnVdVuN1DwIU5lNC+BXYRbq8MgbEBe8sl2l24+9gD36u+0s+E0tjihNmQHkGWyQwJDiJiSgqycLzZAZWzYLAeoK3qA55NrA/hwQBIUsCYLkBWVKic6e4x+FUlvj5UUEq3U4FdEMCDAiVgg2H+46FTrmY4ZzAbBJ0g6HB40dqp3RMw4IeuuGOZu+vSc8b2aggPZ4MQhZ7KgdC+Bdr/6Mtj/XpV9UYyBLB1H7skCZBlNfi9APreBZUUZOFkqzNtgiyTFRIcRMRcdX45VqzdDbdHDhqPs0ySliBQYOh0qX1vFxhgMYpQFBUXVZfh4y+Pac/y38MYkGczQlY42uyePncvguAXXirX1FUMUBTo7CY+WYuTCKCoPCikzCYRYEwnCPKyTWhud6Hd7oXFJPVYcccriV04G4TZJAH+NBa97Qaqyoswe+aYU6o7negAtu5jtxhFdMgKLCYJnPN+d0FXnD8Oz6/+KimCLNMZEhxEr6zZsL+HOmXxxRN79fZRmhxQFA7OVShqoGZFwNYgwGQUUVqQFVzFjh6ag3VbDuNgQwfcfiP7yTY3si0GDMmzoNHvSRWKURIwvMiKy743BgB0RZqMBgaTUdQCAf1pTCSRIddqhMUkBa8rLTDjqgvG6QIOAcBiklCQY0ZbpwdOt9xjxR2vlCHhVv4/unBcj2Pp6C3UfeylBVk4/8xhEXtVTZtUgkVzx6f9e0o0jPPMqLzS3GzvVR+eThQXZ5/SijPAmg37sWbjQTAwXenWS2eNjmmE85oN+/HOZwe74ja6fUQWk4hpE4ZgZkUpJpTlBVOfh+POp//l9/oK6TNXYTUb8OQvvtfj+mWvb+8hCAKpwcNFhIfaOEJXs8mU3C9Wn3+qksnjj/XYBYGhsNAW9hztOIiwDEaQWneOnLDj/206BM7Da7gunlmGS88eA2PIxN4XsqIFhQRUVQIDFM56TXU+kPQrQPqv+gmiP0hwpBlb6xqx6oPdpzyxBYLU1IC7qH/udXnDB/VFSmunB1t2NWLjzgYcOWnv89ovdp/A+JF5EfdfFBmYrMWXBHYwYNrxcAxEECTaBkAQyQAJjjRiR30T3vxoH8BwysFPZqMEt1cOek4FJ2KutRPN81weGdv3nsSm2gbUHWzt4RobziWXMQT97yNta3iRFSfbXbCHlDO1+O0qvRGNIEhERDJFQRPJCAmONGLdlsOQJBZ03ezuLtrXJLSjvgn/+/4etHR4dLUxAgT+12gQsHzNLi3VucIhigzD/bmcQic0RVVRe6AFm2ob8eXekz0Cy6xmCZfMGgWPR8aajYd6jIVzLS36sSYHlr2+PaKJc0F1Gd78aB/ys8WYe9QkIqMsZbFNTkiYk+BIK5ra3cj1u7MGCLiL9jUJAcCLa2rh8nRljO3Nj8DrU8GY6o8QZ4AMNLQ4sXL9XnDOkWM1YdPOBmypa0Sn09drXx1uGe9+dhC3XlqBApsRzZ1dCQgZtN1GS6cHAmM9ytwC4SfOqvIi5OZmBVV1ZoMAySDitQ/2oij38Cn9wAej/noytkn0DQlzDRIcaURRrhl2t08XLBZwF+0vlbY7mMZcI1RuBPIXeWUtvxQDwJgQzFfl9MgwKiJe+HutbmfBAEwoy0Ob3YMTba5gcF5A7eXyKFj9aT2YIKAo14RWu1d7NjQPLkXhyA6J5I5k4pw2qQSjirJi/gOPVwxHotsk+oaEuQblqkojFlSXQZZ52JrHfdW7DmSp7Y1wuw/mz7WkKBxenwq7yxcUGsOLrLjq/HI8+u+zcM91UyErXCc0QmlscaIo1wxJElGQbQJjDD6FB3dNhgEm3YumtnokDEb99WRsk+ibdKobfyqQ4EgjqsqLcOsVVT2S11WVF+kmIafbh4YWJ46cdMDplmE2ir0mJwwkCgxEYAc2Mz4lkJxPQ2AMBdkmPHzjdPzXTTNw8cxRKMjRJrjQia57ynSAYUF1mVaISeFQVa0qoChq9chbOtxweeQefe4vuWCsf+CBPoYTyoNFItok+oaEuQapqtKMgKqmO4GYhXaPjE6XD+DarsHkL+NqEIWgKiqULJMIq8WITqcPsiL3yFzLGJBlkmAxifjxvAkoK8kO2/be79rC7lxysrpSmy9fswscDAZJQE6WliuqpcOD5naX1lBIn/tTO8U6yjsRMRwUN5J8JFPd+ERCgiNDCJ2cwTkMkogcfyoOj09BTpYBLq+C5o6uokdGSYDbq8Lh7kr9ERAUgSh8yZ8CJNyEFvA+Odrk6EXdBVj8yQSryouQZZZQlGf2JybU4Jyjud0DQejZ5770yguqy7DivTp/USauJTU0isHUHQMhETEcFDeSXJAw1yDBkUGEm5ydbh86HD74ZAUlBVkwGYRgnqnQLfmo0mzMqijFjElDkGsz6Z4bEBCa91JX/qqV6/fCJ6thKwEaJAF5NmPQKA+E3yUE6nwMLbLqBEpEaicWaupn6FUfF2YsmTwpEH1DwpwER8YROjk73T40d3QZxo83O3XXigKD2SRiSJ4Fv/3J9LDP6817ySQJEEUBHU6f3wsLwYSHoiD47RgC8qzG4LN6UwOUFGSFrWvel9pp3ZbDyDJLyM/uEnL97VLI1ZIgIiPpjeOqquKNN97AwoULMWXKFMyZMwdLliyB3d53ugoiPJrnlYIOhxfN7R6oqjahh3pVCQJDSYEFw4utKMwx9xmPEfBeCtQFb2rT0pIfb3HB6K+lwNCVP4r77RQ+uaeht7fKdFedXx61kXggxvFYe2IRRLqS9DuOl156CU8++SRuuukm1NTU4MCBA3j66aexb98+vPzyy4nuXsrAOcd3J+yoO9QKl0eBw61XH1lMEmRFW+EzdNW/9viUPlf2Te1aOdnWTg8ArZysz29k/+6EJtwVVa8lklUOi1EKm1W2LzVANCqkgRjHI42biLc6i9RnRLKR1IKDc46XXnoJ11xzDe666y4AwKxZs5Cfn49f/epXqKurw6RJkxLcy9jR3wQRyfm//3krvmvshOK3RgsMMBtFeGW1R5ZYoyTAbBJhlETYXT4oKteM2JzjUENXeuaGZicWL/1YKw2rnfbX7ua6anwMHFzocrcN3cV0/3+nR8bqT+sB9FQD9TbOvlRMgettWUbIPhntTh/cHgW2LAOyswwReb+YDQIamp1QVA7J79klioJO2KzZsB/vbT4cNLi3drqx97s2DCvMwlUXjIt6Qo/kM41EfRZ4TovdC6Oo6QXdPpUEDTEoiA8//PDDie5EbzgcDrS2tuKSSy7BsGHDgscVRcGbb76JWbNmYdy4yLxkXC5vv/WwE0lggvDKKsxGEQ6PjK/3NaEk34KSgqyIzq9YuxsnW509ckz5FK47xhiQYzWCg8PlluHwFz7qs3of9KfD1c5At2P9maI7nT7sOtSKYUVZKPEnIuxvnH29N845GlucsLtk2CwSJFGAwy1DUVQU51lwxblj+xQ+m+tOwOOTATBwzuHyKGAArr5gXMhn8K0/+64WpBiw27i8CvYeaeu1n7212d9Y/7xud9C+wxiDJApQuZaS/uzTh/Z4DmMIvgOLSYRX4X2+v3TDajXB6fT2f2EaEuuxM8aQlWUMey6pbRw2mw0PPvggzjrrLN3xDz/8EAAiFhqpQF/69R31TVi+ZheaOzxo7fTA5ZF76N//b/MhOF2+XnNMBTCIWhJEl0eG16dA5eHTjMSCSJ7n9sg6G0K0dobQ6zudPgiCVka20yUj12ZCYa4Zw4qsuOe6qX2uugPG9MJcSzBaXRQYcqxGnQumylV/uvmQcXKtLG209pBIxhqJrSb0Oe12LxgTgu+A7DTEYJDUqqpwfP3111i+fDnmzJmD8vLyiO/rrZJVstBi9yLbIulcTiWR4XiLE29+tA8enwJJAFSFo7XTA0kUkGUS0djqwup/7sfeI+0R7agEQQCgpQnR6lRwGCQBjDF4fEp/t8cUDm3CbbV7UVysBQ729h5Crwkl9HpZ4RAFgINBUVQYJKHPe3t7To7f04tzDrtL1vXNIInB+iQBTzEOLWuw1SxF1Fa4Nnsb69BiG1o7XDCH2GrcXhlDi21h35lPVrV3wKN/B+lCpowzHPEae0oJjm3btuG2227DiBEj8Lvf/S6qe5O9dGyBzRi2jKnPp8Ji0uIeZIVriQX9HkyANvGu3XgwojYYtMmwu9pK7e5WFQNEATr7R2/9EQWGfJsxWPKyt/cQek0ooddLIvNP6trq3yerfd7b23N6a7fAZoTPp6DT6fW/y677bRYDHG45oraiaXP2lGFYuX4vZIXrXJRnTxkW9p0ZJG3cQPTvIB2g0rHxKR2b1KqqUNauXYsbb7wRQ4cOxauvvor8/PxEdymm9JaXSBIZjJIAm8UAVdWC8hRVExgBA/iIYhsqRvf/PjjgN5KrEARt4su2GKBy3mt51WjJyTKgOE9LWhhBvB3MJklnsJ5Ylofmdje+O2FHQ7MT7XZPn0bt0PeWnWWA6t8NZFukqHI7RZIXakF1GSSRITvLqKsqmJ0lQRSFqFNPRNJmby7KoWq30Ofk2ozgXB3QOyCISEmJHccrr7yCRx55BDNmzMBzzz2H7Oz024qGS2UwZ9oIvP3P/WhscfVQIzEAUycU47Kzx6Cl062lEkFIpb4QsrMMcLh9UHVusQxGg4AsiwFOt4xAliohRP3SnXBeVZwzcGirYYEBWRYDjP7gP0VRcXZlKbbuPoFjzXqjvcCAYf4suqHFpD7b2QCbxQCn2wdZUeBwcVxS07tXUPf3NrIkG7JPhtunIs9qjNijKJJUEqHXBFKYBLyXomkrmjYD1/VXzjbwnFa7F0MLrafUL4LoD8Z5MvsaAW+99RYefPBBXHzxxXjkkUdgNIa38vdHsquqAqicY+/hNmysbcC2PSd0xZWY37XWKAn4yUUTcea44qBHTUuHZiwNpx7S0pYLPVQiEgNsWUbs/a4NBklArs0Ei0lbS3DO4XTL+PG88RHHEJxqvMGy17eHVd3kWY2457qpET0jk1UVAI0/k8cfT1VVUu84mpub8fvf/x7Dhw/HokWLsGvXLt35srIyFBQUJKh3seXoSTs21TZi864GtIQkGhQFhrISGzxeBR6fguI8i25CDnjUGCRRl/cplKZ2N3KyDLoJWZYVNNt9cPtUmI0SjAYhKDQATaVlNghRpeAIrIz1uasir7xHhYsIIjVIasHxr3/9Cy6XC0ePHsWiRYt6nF+2bBkuu+yyBPQsNrTZPdhc24jNtQ04fEKfQmXssBzUVJRi+qQhyOnFlxrommxzrEa4va5er+tw+mAyisgya2qg1k4vRIEhyyxBUTnaHZqwyrEagwZYySDCJ6vocPogyyokSYDFKPab72nF2t1we2QoqooOhxcr1u7G4osn9is8Yp0KnSCIwSGpBcfll1+Oyy+/PNHdiClur4zte09i084G7DrUqvPMGZJnwcyKEtRUlEYcrBWYbCOh3e6FxSSh3e4FwJGXbda5n3q8CpxuOahmevm9Ojg9cjDXlKKo6HSpUJocvbax+tN6OFxaLIEoaMFqDpcXqz+t71dwUK0DgkgNklpwpAuKqmLXwVZs2tmA7d+ehNfXZYiwmiXMmFSCmspSlA/L0fn0A9oKfvWn9WhscQJgKMk361JbLKguw4q1u+Fw9S88vLKKIyfsULmmAmtqdwd9SgWBgXPoVEWKP5pc8GcoZECwXGxvBPopMG3cqt/T9+hJB3bUN0Vs5B1o2pVkJpX7ThChkOAYJDjnONTYiY07G/D5rkZ0hGSYlUQBZ44rRE1lKU4fWwhJ1Lyid9Q3YfUn+9DY6gbAkWszweH2wetTAGheTMdbXFjxXh0WXzIpOOloaqHI+mWzGNDh9AVdeQOofmHAGEJsGVqhV5VrgkC7hUMS+/KzDeSwUnV94kBEKcr7y0mVqmnPU7nvBNEdEhwxpqnNhU27NLtF9/oW40fmYVZlKaZNKEaWv/JdgB31TVjxXh0cbjkYkRwwCgv+ut8AoILD7VWCKSRWrt8LWeUwiAzcn2NJDakF3p0Op08XnBfqviswLX9USUEWPP6zOVYTXB4ZsqJCEgVYTCaU5Ft6HX9JvhnHW1w9Sswa/C66fdlH+iM0tQYAmAwiPP7jyT75pnLfCaI7JDhigMPtwxe7T2DzzgbsPdKuOzesyIqaihLMnFyKwn4KD7m9ChjTYiTAENwVhAqBgLqoqd0d4lGlxUwIDOBMq9ndm4cVoD1fQc9nS6IA2S9RtFgMBklkyMs2RWxzuOqCcVjxXl1wh8UAMIEh3/+MgXhIBVQ8mtuwiByrISh4U8XrijzGiHSCBMcA8ckqvtnfjE07G/B1fZMu8jrXakT1ZM3IXVZi62G3CEeTvza2EHJpMBdSt2y3osBQlGv2TzocihJIma7lagqs9rWdigCfovZ4RqAZg18gMGiqqIDazCurwVri0ejlq8qLsPiSSVi+Zhc8PrlHnfBoPaRCVTxa2hUVLZ3afijLbEgZryvyGCPSCRIcUcA5x7dH2rG5tgFf7D6hK4ZkMoiYOr4YNRUlmDQ6H6IQXTaXolwzOhxef8puDYExKP4ZP7T+t8XIsKC6DKs/2YfjLS7/LkWb+AMqKFHQ8jaF3hc4zkMkR0BYaQJKRXaWWZemYiD1lavKi3DLpZODE75REgac+iJUxZNrM6HFX+q2w+EbUJqPREEeY0Q6QYIjAo43O7TgvNoGnWqBMaBiTAFqKkox5bSiYNW8gbCguixo41DB/TsEDpNBgNenBlVKogAYDFJXB8ABCGCsK0+IEEhc2A2BaV5TuVkGgDF0OLxaRlmRBY+5vUpM0lREmk6jP0JVPBaThIIcM9rtHvjk2PQzXsTqfRBEMkCCow/qDrZg9T/qceC4Pox/VEk2aipLUT1pCHJtppi0FVDxBLyqGOMoKdByDskcPdJwBGwiBf6a4B6/N67kX4WLogDONXdYgTGIAsOQPDP+6+aZMelvpGM61Ymxu4rHYpIgCCyqNCTJQizex2BDLsNEJJDg6INVn+zD4UYtorswx4SZFaWYWVGK4UXWQWkv3MRyzwsbezWqBibVkoIsHDlh1+wjfhWUlpBQ+2PEEFsw91SqQSqe+EEuw0SkkODog2suGIfag604fWwBThuZp3k7xZm+jKqhk2rAI4oBkCQhmIlWkgTdPZGQTKtOUvHED3IZJiKFBEcfTBpdgEmjE5tEsa8Vd+ik6nD5oKocOTYjBAZ/tlwWdU2GZFx1poKKJx0gl2EiUkhw9EIsVt2RPqOv6/pbcYdOqjvqm/DRl8dw/KR9QDUZArXN3T4FBklATpYWLzFYq85k2tkQ5DJMRA4JjjDEYtUd6TMiuS7SFXdVeRFmzxwzoJz8gX54fDJEptWrDsRLWExSzFedybizyXTInkRESsqUjo0nobpexhhMBjGYLiPWz4hFW7EgtK4HB9Mq/EFLUTIYq85kGTfRRSRlagkCoB1HWGKh6430GcmiVw6t69HS4YbKNcHhG6RVZ7KMm9BD9iQiEmjHEYaiXHOPiOtoV92RPiMWbcWCQD8CQXaSyKByDrNBHJRVZ7KMmyCI6CHBEYYF1WVQFBUenwLO+YDSZUT6jFi0FQtC+2E2isjLNqEgx4xbLp08KCvQZBk3QRDRQ6qqMMQidiDSZyRLnEK8+5Es4yYIInoY52GSGqUhzc12qGr6D7W4OHtAXlXpAo2fxp+p44/12AWBobDQFv5czFohCIIgMgISHARBEERUkOAgCIIgooIEB0EQBBEVGeNVJQjxz2ybKDJprOGg8dP4M5VYjr2vZ2WMVxVBEAQRG0hVRRAEQUQFCQ6CIAgiKkhwEARBEFFBgoMgCIKIChIcBEEQRFSQ4CAIgiCiggQHQRAEERUkOAiCIIioIMFBEARBRAUJjhSnrq4OFRUVaGho0B3fsGEDrrzySpxxxhm48MILsWLFigT1MLaoqoo33ngDCxcuxJQpUzBnzhwsWbIEdrs9eM0333yD66+/HlOmTME555yDxx9/HD6fL4G9jh2cc7z66quYP38+qqqqcOmll+Ldd9/VXZOun3047rjjDsydO1d3LJ3HL8syqqqqMGHCBN2/KVOmBK+Jx/gzJldVOrJ//37ceuutkGVZd3z79u247bbbcNFFF+GXv/wltm3bhmXL16Q0yAAAC7FJREFUloFzjptuuilBvY0NL730Ep588kncdNNNqKmpwYEDB/D0009j3759ePnll3Ho0CH827/9G6ZMmYInn3wS9fX1eOKJJ2C32/HQQw8luvunzIsvvoinn34aP//5z3HmmWfin//8J+6++26IooiLL744rT/77rzzzjtYv349ysq6yg2n+/gPHDgAj8eDRx55BKNHjw4eFwRtDxC38XMi5fD5fPy1117jU6ZM4TNmzODjx4/nx48fD57/yU9+wq+++mrdPcuWLePTpk3jHo8n3t2NGaqq8unTp/OHH35Yd/y9997j48eP57t27eIPPPAAP++883TjXLlyJZ80aRJvaGiId5djitfr5dOnT+f/9V//pTv+4x//mF977bWc8/T97LvT0NDAp0+fzs8991w+Z86c4PF0H/+aNWv4xIkTudPpDHs+XuMnVVUKsm3bNvzxj3/E4sWLcffdd+vOeTwebN26FfPmzdMdnz9/Pjo6OrB9+/Z4djWmOBwOXHrppfj+97+vOz527FgAwOHDh/HZZ5/hggsugNFoDJ5fsGABFEXBhg0b4trfWCOKIv73f/8Xt9xyi+64wWCAx+NJ68++Ow8++CDOPvts1NTUBI9lwvjr6upQVlYGi8XS41w8x0+CIwUpLy/Hhx9+iDvuuAOiKOrOfffdd/D5fBgzZozu+KhRowBoW91UxWaz4cEHH8RZZ52lO/7hhx8C0N7L8ePHe4y9oKAANpstpccOaOqICRMmoKSkBJxzNDU1Yfny5di4cSOuueaatP7sQ3nrrbdQW1uL3/72t7rjmTD+PXv2wGg04qabbsKUKVMwffp0PPTQQ7Db7XEdP9k4UpCioqJez3V2asXqbTZ9kXmr1QoAOiNyOvD1119j+fLlmDNnDnJycgD0HDugjT+dxv7BBx/gF7/4BQDg/PPPx6WXXoq6ujoA6f3ZHz16FEuWLMGSJUtQUFCgO5cJ3/3du3fDbrfj6quvxm233YadO3fimWeewYEDB/DrX/8aQHzGT4IjzeD+8iqMhS/CEjCipQPbtm3DbbfdhhEjRuB3v/sdvF4vgPBj55yn1dgnT56M1157DXv27MFTTz2FW265BXfeeSeA9P3sOed44IEHcN5552H+/PlhzwPpO34AeOKJJ5Cbm4sJEyYAAKZPn47CwkL85je/wWeffQYgPuMnwZFmZGdnA+i5ugj8HTif6qxduxb33XcfRo8ejZdeegn5+flwOBwAwq+snE5n2owdAEaOHImRI0di+vTpsNlsuPfee4MTZ7p+9itXrsSePXvw7rvvBj0JA2OWZTkjvvszZszocez888/X/R2P8ZPgSDPKysogiiIOHz6sOx74u7v+MxV55ZVX8Mgjj2DGjBl47rnngj8Iq9WKkpISHDp0SHd9c3Mz7HZ7yo+9ra0Nn376KWpqalBSUhI8PnnyZADAkSNH0vqzf//999Ha2opzzjmnx7mKigo8/PDDaT3+5uZmfPzxx5g5cyZGjhwZPO52uwEAhYWFcRt/6u/dCB0mkwnTpk3DBx98EFyNAdqPLjs7G5WVlQns3anz1ltvYenSpbjooovw0ksv9VhFnX322fjkk0+CaitAG7soimFXa6mEqqq47777sGrVKt3xgIri9NNPT+vP/j//8z+xevVq3b8LLrgApaWlWL16NRYsWJDW42eM4aGHHsJrr72mO7527VqIoohZs2bFbfziww8//HDMnkbEnbq6Onz00Ue48cYbg0ax0tJS/OlPf0J9fT0sFgv+/ve/47//+7/x85//HNXV1Qnu8cBpbm7GzTffjJKSEtx1111obm5GQ0ND8J/RaMTkyZOxYsUKbN26Fbm5ufj000/x6KOP4uqrr8bChQsTPYRTwmKxoKWlBf/zP/8DSZLg9Xrxzjvv4Nlnn8UVV1yBK6+8Mm0/ewDIz89HSUmJ7t+GDRtw4sQJ3H333bBYLGk9fovFgra2NqxcuRKqqkJVVbzzzjt4+umncd1112HhwoXxG3/MIkKIhPDXv/61RwAg55x/8MEH/Pvf/z6vqKjgF154IX/55ZcT1MPY8be//Y2PHz++139///vfOeecf/HFF/zqq6/mlZWV/Hvf+x5/7LHHuNfrTXDvY4PX6+XLly/n8+bN45WVlXzOnDn8xRdf5IqiBK9Jx8++N+69915dACDn6T3+wOc/f/58XllZyWfPnp2Qz59xHrKnIQiCIIh+IBsHQRAEERUkOAiCIIioIMFBEARBRAUJDoIgCCIqSHAQBEEQUUGCgyAIgogKEhxExtPc3Ayn0xn1fXa7HS0tLVHfd9999wWT1EXDM888gwkTJuDIkSN9Xvf2229jwoQJ2LJlS0R/E0S0kOAgMpp//OMfWLBgQdQCYOfOnbjooovw7bffDlLPBs706dOxbNkylJeXJ7orRJpCSQ6JjGbHjh3o6OiI+r69e/fixIkTg9CjUyeQOZcgBgvacRAEQRBRQYKDyFjuu+8+PPvsswCA2bNn4/rrrweglef893//d0ybNg1VVVX44Q9/GCxPC2i2hvvvvx8AcMMNN+DCCy8Mntu0aRNuvvlmVFdXo6KiAt/73vfw0EMPDWhX0xv79+/HDTfcgKqqKpx//vl46qmn4PP5gufJhkEMNqSqIjKWa665Bna7HevXr8f999+P0047DTt27MANN9wAm82GG2+8EVarFe+88w5uv/12PPTQQ1i0aBHmzp2LkydPYtWqVbjttttw+umnAwA2bNiAn/70p5g6dSp+8YtfgDGGzz77DKtWrYLP58OSJUti0u9f/vKXqK6uxr333ovPP/8czz//PI4fP46lS5fG5PkE0R8kOIiMZcqUKZgwYQLWr1+POXPmYMSIEfjhD38IxhhWr16N0tJSAMC1116La6+9FsuWLcNFF12EiRMn4swzz8SqVaswa9asYLrqV199FUOHDsUrr7wCo9EIALjuuutwzTXX4P3334+Z4DjvvPPw5JNPAgAWLVqE+++/H2+//TZuvPHGAXlrEUS0kKqKIPw0NTXh66+/xmWXXRYUGoBWHOumm26C2+3Gxo0be73/xRdfxF//+teg0ACA1tZW2Gy2Abn79sZNN92k+zugYvvHP/4RszYIoi9ox0EQfo4ePQogfInNgGvrsWPHer1fFEV89913eOqpp7Bv3z4cPnwYjY2NMe/n2LFjdX+XlZUBQL/xHQQRK2jHQRB++ipNo6oqAMBgMPR6zZtvvomrr74amzdvxujRo3HzzTfjL3/5S8wrDzLGdH8H+i2KYkzbIYjeoB0HQfgZPnw4AM1rqTsHDhwAAJ0KKxSPx4OlS5eiuroaK1asgCR1/bSeeuqpmPbz6NGjOO2003r0LbDzIIjBhnYcREYjCNpPgHOO4uJiVFZWYs2aNWhoaAhe4/V6gwbvs88+W3dfYCfidrvhcrkwevRondCoq6vD559/DgCQZTkmff7LX/6i+/uVV14BY0znFkwQgwntOIiMpqCgAADw0ksv4dxzz8WDDz6In/zkJ7jqqqtw7bXXwmq1Ys2aNaitrcWDDz6InJwc3X1vvPEGmpqasHDhQpxxxhl4++23YbPZMGbMGHz77bd46623gkLG4XAgNzf3lPv87rvv4v9v7w5VHAaiKAyftckDRFRUxFTVx4eWkpeIKFWZB6gvVKdQVaitalUhUBPihrxKbVREdt2yrCgZQsnC/p+euVx3YC7caZpG8/lcVVWpLEut12tNp9PBtYE+CA78a0mS6PF46Ha7qa5rFUWhy+Wiw+Gg8/msrus0m810PB4Vx/H3vSiKtFqtVJalrLVaLBbK81z7/V7X61Vt22oymWiz2SgMQxljZK3Vcrkc3PPpdNJut9P9flcQBNput0rTdHBdoK+Pz1cTQQAAfmHGAQBwwlMVMKLn89nrnOd58n3/zd0A/fBUBYyo74qQLMtkjHlzN0A/BAcwolcrTH7ijw38JQQHAMAJw3EAgBOCAwDghOAAADghOAAATggOAICTL+m7ioGRpCb+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(data['total_bill'], data['tip'], ci=None)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lineplot(data['total_bill'], data['total_bill'] * 0.1437319)\n",
    "ax = sns.scatterplot(data['total_bill'], data['tip'])\n",
    "ax.set_ylim([0, 11])\n",
    "ax.set_xlim([0, 53])\n",
    "fig = ax.get_figure()\n",
    "fig.savefig('14_percent.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1d304061ec8>]"
      ]
     },
     "execution_count": 48,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data['total_bill'], data['tip'])\n",
    "total_bill_values = np.linspace(0, 50, 100).reshape(-1, 1)\n",
    "predicted_tips = lm.predict(total_bill_values)\n",
    "plt.plot(total_bill_values, predicted_tips, 'r--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = sns.regplot(x=\"total_bill\", y=\"tip\", data=data)\n",
    "ax.set_ylim([0, 11])\n",
    "ax.set_xlim([0, 53])\n",
    "fig = ax.get_figure()\n",
    "fig.savefig(\"sns_tip_model2.png\", dpi=300, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(data['total_bill'], data['tip'])\n",
    "\n",
    "total_bill_values = np.linspace(0, 50, 100).reshape(-1, 1)\n",
    "predicted_tips = lm.predict(total_bill_values)\n",
    "plt.plot(total_bill_values, predicted_tips)\n",
    "fig = plt.gcf()\n",
    "fig.savefig('scikit_plot_tips.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_squared_error\n",
    "\n",
    "thetas = np.linspace(0, 0.3, 101)\n",
    "errors = [\n",
    "    mean_squared_error(data['tip'], data['total_bill'] * theta)\n",
    "    for theta in thetas\n",
    "]\n",
    "plt.plot(thetas, errors)\n",
    "plt.xlabel(r'$\\theta$')\n",
    "plt.ylabel('MSE')\n",
    "fig = plt.gcf()\n",
    "fig.savefig('MSE_vs_theta.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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DLX4lbR04cpm2+CVEGzyYdDcy4OH5CW5sxxkQVCYawGmwCSYE2OP89XKU10nYjkMIUdC17BpklzRizng3mBjz2Y4zIKhMNMTsZ1xhyOdhb0KeViwdQ4iuapN2Yt/5fDgNEiI8QHvmQalMNISp8e8Lv90pFCHjbj3bcQgh/XQ8pRgN99qxcLIXuFzNnnR/FJWJBpk40h52VsbYm5CHzi4Z23EIIXKqErXgzNUShPjZwtPBnO04A4rKRIPo8X7f4remoRXxaWVsxyGEyIFhGMSeywVfn4sXwnsuZKvpqEw0jJ+bFUa4W+FociGaJFK24xBC+uhmXh1uF4rwXJgbzITatzU3lYkGio7wREenDL8k3mU7CiGkD6QdXdibkAd7awEmjdSeSfdHUZloIFtLY0SNdsTl3ypRVNXMdhxCSC9OphajrqkNC6O8oMfTzj+72vlT6YAZIS4wMdZHbDxdKkyIOqtpbMXJ1BKM8RmEoc7as7L5H1GZaChjQz3MneCO/LImXMmqZjsOIeQJ9sbngcflIHqSJ9tRlIrKRIOFDbeD82ATHLhwF+3SLrbjEEL+ICO/Dun5dZgV6gILE+2bdH8UlYkG43I5mB/piYZ77TiRWsx2HELIIzo6uxAXnwc7K2NEBTmyHUfpqEw0nJejOcYNG4zTV0pQ29jKdhxCyH2nr5SgprEVCyK1d9L9Udr/E+qAFyZ6gMflYB9t8UuIWqhrbMXxX4sxeugg+Lpash1HJahMtICFiQFmhDjjRm4t7hSK2I5DiM6LS8gDhwO8NMmD7SgqQ2WiJSYHOWKQuRFi43Np3S5CWPTb3TrczKvDrFBXWJoash1HZahMtIS+Hg8vRXiisr4F56/Tul2EsKGjswux5/Jga2mMyTow6f4oKhMtMsLDCn5uljiS/Pu+0oQQ1Tp1f9J94WTdmHR/lG79tFqOw+FgfoQnpB0yHKR1uwhRqdrGVpz4tRhBQwfB10U3Jt0fRWWiZeysBA/X7SqspHW7CFGVuPg8cDkcROvQpPujqEy00MxQF5gI+Ig9lwsZrdtFiNKl592/0z3MRacm3R9FZaKFjAz08EK4O+5WNOPX21VsxyFEq0k7uhAbn/v7ne6jdWvS/VFUJloq2M8WbkNM8fPFu2ht72Q7DiFa68Hy8osme+vcpPujdPcn13JcDgcLo7zQJJHiWEoR23EI0UrVDS04mVqCscMGw0eLl5fvCyoTLeZqZ4owfzucu1aKynoJ23EI0SoMw2DPuVzo8Th4caJuTro/ispEyz0/wR18fS7iEmgTLUIG0o3cOtwuEGF2mKvWLy/fF1QmWs5MwMdzoa64XSBCRn4923EI0Qrt0i7sTciFg40AEaMd2I6jFqhMdMCkUQ6wszLG3oQ8dHTSul2EKOpYShHqm9uxaLI3eFz6MwpQmegEPR4XCyK9UNPYirPXStiOQ4hGq6yX4MzVEoT62cLL0ZztOGqDykRH+LpaItDTGsdTitFwr53tOIRoJIZhsPtsLvj6PMyjSfduqEx0SHSEJ7pkDH6+SJtoEdIf17JrkFXcgLnj3WAm4LMdR630WiZr1qxBWlpat2MymQzZ2dlobe25TezRo0fh4+PTpyeXyWSIi4vDzJkzERgYiMjISGzatAlisfiJ53R2duKrr77ChAkTMGLECCxYsAC//fZbn55P1w0yN8LUsU749U418soa2Y5DiEZpbe/E3oQ8OA82wcRAe7bjqJ1eyyQ+Ph6VlZXdjjU1NWHOnDlIT09X6Mm3b9+Ov//97wgPD8e3336LV155BYcPH8Zf//rXJ56zceNG7Ny5EytXrsSXX34JHo+HpUuXorS0VKEsuuLZcc6wMDHAnnO5kMnoUmFC+urI5UI0iaVYNMULXC6H7Thqp98fcyl6zwLDMNi+fTuio6Px5ptvIiQkBAsXLsT777+Py5cvIysrq8c5ZWVl2LdvH9555x0sWrQIkyZNwg8//AAzMzNs375doTy6woDPQ/QkD5RUi5H0WwXbcQjRCGU1YsSnleGZEUPgPsSM7ThqibU5E4lEglmzZmHGjBndjru5uQEASkp6XnWUmpqKrq4uTJky5eExPp+P8PBwJCUlKTewFgkaOghejub4JbEAkrYOtuMQotZkDIOfzubA2FAP88Ld2Y6jtlgrE6FQiA0bNmDUqFHdjsfHxwMAPDx6XilRUFAAMzMzWFp233jG2dkZFRUVaGtrU15gLcLhcLAg0hOStg4cvlTIdhxC1FrKrSrklzVhXrg7hEb6bMdRW3psB3hURkYGvvvuO0RGRsLdvecrALFYDKFQ2OO4QCAA8Pu7HUPDvu8lYGXV83v1lY2NSb/PVQc2NiaYGuyCM6nFmD3REy52pmxHUpimj4m20uRxEbdIcTDpLoY6W2DOJO2ZK1HGmKhNmVy/fh2vvvoqHBwc8PHHHz/2MU+ap3lwnMORb6Dr68X9moS2sTFBbe09uc9TN9OCHJF0owzf7r+Jt+YHyv3vp060ZUy0jaaPy64zOWiWSLHuhRGor3/yVaaapL9jwuVynvoCvE9l0tjYiIqK/03WNjU1AQBEIlG34wDQ0NAgd8iTJ09i/fr1cHFxwfbt22Fh8filnIVCISSSnqvfPjj2uHct5MmERvqYM94Nu8/m4npOLUYPHcR2JELURmFlMy7eLEfEKAc4Ddbcd1eq0qcy+eSTT/DJJ5/0OB4TE6NwgB07dmDz5s0YM2YMvv32W5iYPHnQ3Nzc0NjYiKamJpiZ/e+KiuLiYjg4OIDPp5uI5BUeYI/E9ArsO5+H4e5WMNDnsR2JENbJZAx2ncmBqYCP2c+4sR1HI/RaJnPmzFHakx84cACffvoppk+fjs2bN/daBiEhIQCAM2fO4MUXXwQASKVSJCYmIiwsTGk5tRmX+/tk/ObYmziVWky/OIQASMyoQFHVPayaNQzGhmozG6DWev1X2rRpk1KeuL6+Hhs3boS9vT0WLlyIzMzMbl93cnICn89Hfn4+nJycYGlpCXt7e8yZMwcff/wxWlpa4OzsjB07dqCpqQkrVqxQSk5d4O1kgTE+g3DqSgnChtvB2tyI7UiEsKZZIsXBi3cx1MkcY30Gsx1HYwxo5dbW1uLIkSM4fPgwjh8//tTHXrp0Ca2trSgvL8fChQt7fH3Lli2wtbXFkiVLsGnTJsydOxcA8NFHH8HU1BTfffcdWlpa4Ovrix07dsDZ2XkgfxSd8+JED6Tn12HfhXz8Zc5wtuMQwpoDF/PR3tGFRZO9NfqiFFXjMAreyt7R0YGEhAQcOnQIycnJ6OzsBI/Hw507dwYqo9Lo+tVcf3QspQiHkgoQ81IAhrlY9n6CGtHWMdF0mjYuuaWN+HTPDUwf56y1NyiyejXX49y+fRuHDh3C8ePH0dzcDIZhYG1tjeeffx7R0dH9/baERVPHOOLybxXYcy4XHy4bAz0eLSpNdEdnlwy7zubAytQAM0Nc2I6jceQqk/r6ehw5cgSHDh1Cfn4+GIZ5+Dbwtddew+rVq6GnR5NVmkpfj4eXIjzxzcFbOH+jHJODHNmORIjKJFwvQ3mtBGvmDocBn65qlFevf/k7Oztx/vx5/PLLL7h8+TI6OzvB5/MxYcIEREVFwdvbG/PmzcPQoUOpSLRAgIc1/FwtceRyAcYOG0x7NhCd0HCvHYcvF8Lf3QqBntZsx9FIvf71f+aZZ9DY2AihUIioqChERUVhwoQJD5cwKS8vV3pIojocDgfzIz3xtx+u4ucL+Vg+YxjbkQhRuriEPHR1MVgQ6UmT7v3U64fiDQ0NMDIywsyZMzF16lSMGzfuYZEQ7WRnJcCUMU5Ivl2F3FLaRItot1sF9UjLrsHMEGcMsjBmO47G6rVMdu7cienTp+P48eNYu3YtwsLCsGDBAuzcuZPelWixmSEusDQ1wO6zOeiSydiOQ4hSSDu6sPtsDmwtjTF1LN1eoIhey2TcuHH4+OOPcfnyZXz99deIjIzEnTt38OmnnyIyMhIrVqwAh8NBS0uLKvISFTHg8zA/whNltRIkXKcXDUQ7Hf+1GLWNbVg8xRv6enT1oiJ4H3zwwQd9eiCPB3d3d0ybNg2LFy+Gs7MzJBIJsrKyIJPJkJCQgLS0NOjr68PFxQU8nvpfDdHaKkV/7rIRCAzQ0iId+EBqxs7KGAWVzUi5XYUQPzsYGajvBRa6MiaaRp3HpbJegu+PZWLcMFtMGePEdhyV6e+YcDgcGBs/+YIchW9arK2txYkTJ3Ds2LGHNyqamZnhypUrinxblaCbFntX3dCC/9t+FaO8bbB6li/bcZ5Il8ZEk6jruDAMgy2xN1FaI8Ynq8bBVIeuWlTWTYsKv6+zsbHB0qVLcfDgQZw5cwZr1qyBubm5ot+WqInBFsaYPs4JVzKrkVkkYjsOIQMi+VYVckob8cJEd50qEmXq9XOLd999V+5vOnLkyH6FIepp+jhnpN6pxu6zv98ZT58tE012r0WK/Rfy4eFghmdGDGE7jtbotUwOHTr08Lrrvn4ixuFwlLbaMFE9vj4PC6K88NWBDJy9VoJng13YjkRIv+0/n4/W9k68PMUbXLqnZMD0WiZeXl7Izc2FpaUlIiIiEBUVheDgYOjr66siH1ET/u5WGOVlg2PJRRjrM5iWqScaKau4Acm3q/BssDPsbWhn1oHU6+cVR48eRXx8PFatWoWCggK8+uqrCA4ORkxMDM6cOYO2tjZV5CRqYP79u4Nj4/PYjkKI3KQdXfjv6WwMMjeihRyVoE/Xejo4OGDp0qVYunQpRCIR4uPjER8fj5iYGPB4PISEhCAqKgqTJk3qtp0u0S6WpoaYFeaCAxfuIj2vDgG0hhHRIMdSilDT0IqYlwLAp+2pB5xClwaLxWIkJiYiPj4eSUlJaG9vx+jRozF58mQsWLBgIHMqBV0aLL/OLhk+2HEN0o4u/H3FWLXZM16Xx0Sdqcu4lNWI8eHOaxg3bLDOrzenlpcGC4VCPPvss/jyyy+xd+9ejBs3Dqmpqfj73/+uyLclakyPx8XiyV6oa2rDiV+L2I5DSK9kMgY7T2fDyEAP0RGebMfRWgrd0pyeno7z588jISEBBQUF4HK5CAoKQmRk5EDlI2rI28kCwb62OJVagmBfW9hZ0cKfRH1duFmOgopmrJw5DEIjunBIWeQqE6lUipSUFCQkJODChQuor6+HoaEhQkJCsGLFCkycOJFuWNQRL076fc/4XWdy8Nb8QFq2m6glUXMbfk68C19XS4wbNpjtOFqt1zJpaGjAxYsXkZCQgOTkZLS2tsLCwgLh4eGIjIxEWFgYDAwMVJGVqBEzAR/zwt2x60wOUm5XIXS4HduRCOmGYRjsPpsLhmGwZIo3veBRsl7LJDQ0FAzDwMHBAdHR0YiMjMSoUaNoYAgmBAxByq1K7DufjxEe1vQRAlEr13NqkZ5fhxcnesCG7otSul6v5ho6dOj/HtzHAuFwOMjMzFQsmQrQ1VyKe3CVTLCfLZZN92EtB42JemJrXCRtHdjw/RWYCw2w4eVR4HFpCaAHlHU1V6/vTObMmSP3kxLd4TBIiMlBjjh1pQShfrbwdrJgOxIhOHDhLu61dGDtCyOoSFSk1zKhNbZIb2aFuuJadg1+OpODD16hhSAJu7KLG5CUUYGpY5zgbGvCdhydQb/1RGEGfB4WTfZGZX0LTl8pZjsO0WHSji7svL9kynPPuLIdR6dQmZAB4e9uhaChg3AspRjVItrCmbDjSHIhahpa8fJUb7VZnUFXUJmQATM/0hP6ehz8dCanz9sVEDJQiqvu4cyVUoT528HHxZLtODqHyoQMGHOhAeZNcEdWcQN+vVPFdhyiQzq7ZNhxKgtCY31ET/JgO45OojIhA2pCoD3c7U2xNyEfzS1StuMQHXH6SglKqsVYPNkbAkO634kNVCZkQHE5HCydOhSt7Z3YS/ueEBUor5PgaHIhgoYOwihvG7bj6CwqEzLg7G2EmBHigtTMamTk17Edh2gxmYzBjpNZMOTrYWGUF9txdJralElWVhZ8fX1RVfX0z9qPHDkCb2/vHv999NFHKkpK+uLZYGfYWwuw62wOWts72Y5DtNS5tFIUVDRjQaQnTAV8tuPoNIWWoB8oBQUFWL16NTo7e/+jk52dDWdnZ2zZsjPH6EcAABhrSURBVKXbcWtr2vVPnejxuFg6bSg+2XUdP1+8i8VTvNmORLRMtagFvyQVIMDDGmNpRWDWsVomnZ2d2LdvH7744gvo6/dt0iwnJwe+vr4ICAhQcjqiKHd7M0QFOeLstVKMHjoIPs601AoZGDIZgx9OZkGfx8ViWhFYLbD6Mdf169fx+eefY9myZYiJienTOdnZ2fD2ple5mmLOeDcMsjDCjpNZaJPSx11kYMRfL0N+WRMWRHnCwoS2wFAHrJaJu7s74uPjsWbNGvB4vd+tWlNTg/r6emRmZmLq1Knw9fXFlClTcPjwYRWkJf1hoM/Dsuk+qG9qw8GLBWzHIVqgWtSCXxLvYoS7FYJ9bdmOQ+5j9WMueec5srOzAQBlZWV46623YGBggMOHD+Odd95BV1cXnn/+eWXEJArycjRHxGgHxKeVYZS3DYbSx12kn2QMgx9PZkGPx8WSqUPp4y01ohYT8H3l5+eH//znPwgKCoJQ+Pu6+mFhYaivr8c///lPucvkaWvz98bGhlYjlcfq50fgTlEDdp7OxjcxE2GshBvLaEzU00COy5Gku8gra8K6+YHwcqOLbvpLGb8rGlUmlpaWmDhxYo/jEyZMQEpKCkQiESwt+74mD22OpVqvTBuKTbuv4+u4G1g+Y9iAfm8aE/U0kONSJWrBTycyMcLdCn5O5jTe/aSszbHU5j6Tvrh58yYOHDjQ43h7ezv09PRgYkKvTNWZh70ZZoa4IPl2Fa5l17Adh2gQmYzBjyfo4y11plFlkp6ejg0bNjycOwEAmUyGM2fOYOTIkX2+vJiwZ0aIC1ztTPDT6Ww03GtnOw7REOfSSpFf3oT5kXT1lrpS6zIRiURIT0+HWCwGAMydOxf29vZYs2YNjh8/jgsXLmD16tXIzc3t86XFhF16PC5WzvRFR5cM249nQkZL1ZNeVNRJcDCxACPcrRDiR1dvqSu1LpOLFy8iOjoad+7cAQCYmZlh165d8Pf3x6ZNm7B27Vq0tLRg586dGDFiBMtpSV/ZWhpjfoQnsoobcOZKCdtxiBrrvP+iw5DPw9Jp9PGWOuMwOryLEU3As4dhGPzr8G2k59XhvcWj4GpnqtD3ozFRT4qOy9HLhTh8uRB/mu2HoKGDBjCZ7qIJeKJVOBwOlk4bCjMhH9uO3qHFIEkPRVXNOJZShHHDBlORaAAqE8IagaE+Vs30RW1jK/acy2U7DlEjHZ1d2H48CybG+lg4mZaW1wRUJoRVXo7mmBnigpTbVUi5Xcl2HKImDiYWoKJOgmXTfWjnRA1BZUJYNyvUFd6O5th1JheV9RK24xCWZRc34Ny1UkwMtIefmxXbcUgfUZkQ1nG5HKya5Qt9PS7+ffgOpB1dbEciLGlt78QPJzJhY2GEFyd6sB2HyIHKhKgFCxMDrJjhg7JaMfadz2c7DmFJbHwuRPfasXLGMBjwe19JnKgPKhOiNvzdrTF1jBMu3CzH1axqtuMQFbueU4PkW1WYPs4Z7vZmbMchcqIyIWpl7gQ3uA8xxc5T2ahpaGE7DlGRRnE7/ns6B862JnguzJXtOKQfqEyIWtHjcbH6OV/wuBz8+/AddHTK2I5ElIy5v0eJtKMLq2YOgx6P/ixpIho1onaszYyw7FkfFFffw36aP9F652+U43aBCC9M9ICdlYDtOKSfqEyIWgr0tMHkIEck3Cij+RMtVlEnwYEL+fBzs8SkkfZsxyEKoDIhamteuDs87M2w41Q23X+ihTq7ZPju2B3w9XlYPt2HFnHUcFQmRG3p8bh49Tlf6PO4+Neh22iX0v0n2uTQpQKUVIvxyvShMBPSHiWajsqEqDVLU0OsmjUMFXUS7DqbAx1e5FqrZBc34HRqCSYEDEGgpw3bccgAoDIhas/P1QozQ39fvysxo4LtOERBkrYObD+RiUGWxnhpkifbccgAoTIhGmFWqCv8XC0Rey4XhZXNbMch/cQwDHaeykaTWIpVM+kud21CZUI0ApfLwcqZw2Aq4ONfh25D3NrBdiTSD4kZFbieU4u5E9wU3hCNqBcqE6IxTIz5+PPs4WgUt+P7Y5n92iWTsKe8ToK98XnwdbHAlDFObMchA4zKhGgUtyGmWBDpiVsF9Th8uZDtOKSPpB1d2Hbk/mXAM4aBS5cBax0qE6JxwgPtEeZvh+MpRbiRW8t2HNIHsfG5KKsVY8UMH5jTZcBaicqEaBwOh4PFk73gameC7cczUVFHNzSqs+RblUjKqMSzwc7wd7dmOw5REioTopH09Xj4y5zh4Otx8c0vt2hCXk0VVzVj19kceDuaY/YztBqwNqMyIRrL0tQQf54zHHWNrfhsdxpNyKuZ1vZOfPrfazDk691fCZr+3GgzGl2i0bwczbFoshduZNdg/wVaYVhdPFhWvqJWjNWzfGmeRAfosR2AEEVNCLBHvViK45cLYW8twDMjhrAdSeedulKC6zm1WDbTFz7OFmzHISpA70yIVlgxyw/DXCzw05kcZBWJ2I6j0+4UinAw8S7G+AzC7AnubMchKkJlQrQCj8fFn2b7wdbSGFsP3UJJ9T22I+mkalEL/nPkNoZYC/DKNFpWXpdQmRCtITDUx7oXR8CQr4cvD2SgrqmV7Ug6pVkixT/2p4PD4eC1ucNp3S0dQ2VCtIqlqSHWvTgC0g4ZvtyfgeYWKduRdEK7tAv//Pk3NIml+Os8fwyyMGY7ElExKhOidRxshHj9+eGob2rD53E3cY8KRam6ZDJsO3oHRZXNWDXLF+72ZmxHIiygMiFaydvJAq/N80d1Qyu+2JtONzUqiUzG4IfjWUjPr8OCKC+M9KKNrnSV2pRJVlYWfH19UVVV9dTHSSQSfPjhhwgNDUVgYCBWrlyJoqIi1YQkGsXXxRKvzR2OinoJFYoSyBgGO05mITWzGs9PcEPEKAe2IxEWqUWZFBQUYPXq1ejs7Oz1sevWrcPp06cRExODzZs3o7q6GkuWLMG9e3T1DunJz80Ka+YOR3mdGJ/F3aQ5lAEiYxj8dDoHyberMDvMFc8Gu7AdibCM1TLp7OzEnj17MG/ePLS3t/f6+LS0NCQmJmLz5s2YM2cOJk+ejJ07d+LevXuIi4tTQWKiifzdrfH6PH9Ui1qwJfYmGsW9/79Gnkwm+323xKSMCjwb7IyZoS5sRyJqgNUyuX79Oj7//HMsW7YMMTExvT4+OTkZAoEAoaGhD49ZWloiKCgISUlJyoxKNJyfqxXWvTgC9U1t2LznBkTNbWxH0kidXTJ8fzwTl3+rxKxQF8wd70b3khAALJeJu7s74uPjsWbNGvB4vV+TXlBQAGdn5x6PdXJyQmEhbZREns7byQJvRgeguUWKTbtvoKahhe1IGqWjU4ZtR+7gyv05ktnPUJGQ/2G1TKytrWFlZdXnx4vFYgiFwh7HBQIBxGLxQEYjWsrDwQxvzQ9Em7QTn+65QXuh9FG7tAtfH/wN13NrMT/Ck+ZISA8atdAjwzx5iXFuP5a3trLqWUx9ZWNj0u9ziXL0dUxsbEyw2doEG7al4LO9N/HhymC4O5grOZ3mErdIsSUuFbklDXj9xQBEjXWW63z6XVE/yhgTjSoToVCIsrKyHsclEslj37H0pr5e3K89MGxsTFBbS1ePqRN5x8RYj4N35gfis7038e6/krH2BX94UqH00HCvHV/uz0CVSII/zfZDgJulXP/O9Luifvo7Jlwu56kvwNXi0uC+cnV1RWlpaY93KMXFxXB1pV3ciHwGWxrj3YWjYCrg44u96bhdUM92JLVSWNmMj/57DbVNrfjrvBEY5T2I7UhEjWlUmYSFhaG5uRkpKSkPj4lEIqSlpSEkJITFZERTWZkZ4t2FI2FraYx//vwbkm9Vsh1JLaRmVuHTPTegz+Pi/y0eBV9XS7YjETWn1mUiEomQnp7+cHI9KCgIY8aMwRtvvIEDBw7g3LlzWLp0KUxMTDB//nyW0xJNZSrg4+0FgfByNMcPJ7LwS9JdyJ4yP6fNumQy7D+fj++OZsLVzhQbXh4NB5v+zy0S3aHWZXLx4kVER0fjzp07D49t3boVkyZNwpYtW7B+/XrY2tpi586dMDOjxeVI/xnfX75+/IghOJ5SjP8cvo12aRfbsVSqUdyOz+LScfpqCSaOtEfMSwEwNeazHYtoCA7ztEuktBxNwGuPgRoThmFw7lop9p3Ph72NAH+ZOxyDdWA59awiEb47lolWaSdenjoUwb62A/J96XdF/dAEPCEqwOFwMHmME9ZFj0DDvXZ8tDMNN/Nq2Y6lNJ1dMhy4kI/P96bD2FAPG5aMHrAiIbqFyoSQx/BztcL7rwRhsIURvjl4C3sT8tDRqV0fe1XWS7Bx13WculKCCQFD8LelQTQ/QvpNo+4zIUSVrM2M8O6ikdh3Ph9nr5Uis0iEVbN8Nf4PrkzG4Oy1UvySVAADfS7WzB1O+5AQhVGZEPIU+no8LJrsDX93K/x4Igsf7UzD3PFumBzkCC5X89alqqyXYMfJbOSXNyHQ0xpLpnjDTGjAdiyiBahMCOkDf3drfLR8LP57Ohv7L+TjWnYNlj3rA3trAdvR+kTa0YXjvxbjVGoxDPR5WDljGMb5DqaFGsmAoTIhpI9MBXysmTsc17JrsPtsLj7ccRXTxjpjerAzDPR7X/WaDQzDID2vDnvP56G2sQ3BvrZ4cZIHzAR0yS8ZWFQmhMiBw+FgjM9gDHW2wN6EPBxLKULK7Uq8FOGJkV42avVKP7+8Cfsv5CO/rAl2VsZ466UA+LjQnexEOahMCOkHU2M+Vs30xYQRQ7DnXC6+PXQb3o7mmDfRHe5D2L2BtqCiGceSC5Fxtx5mAj6WTPHGMyPswOvHytqE9BXdtEg3LWoFNsekSyZDYnoFjl4uRHNLB0Z522DOM24YosL5FIZhkFvaiBOpxbhdIILAUA+Txzhh8mhHGPDZ+wiOflfUj7JuWqR3JoQoiMflYtJIB4T42eLstVKculKCGzm1GDNsMGaGuCi1VDq7ZLiWVYOz10pRXH0PQiN9zAt3x8RAexgZ0K83UR36v42QAWLI18OsUFdMDLTHmaulSLhehquZ1QjwtEZ4oD18XS3BHYA5FYZhUFR1Dym3qnAlqxri1g7YWRljyVRvBPvaqu3FAES7UZkQMsBMjPmYF+6OKWMccfZaKZIyKnAzrw7WZoYYPXQQPB3M4OlgDqGRfp+/Z2t7J3JLG3GroB6/3a1HXVMb9HhcjPSyRuhwuwErKkL6i+ZMaM5EK6jzmHR0ynAzrxaJ6RXIK2tEZ9fv/89ZmxliiLUAdlbGMBcawECfBwN9HjplMohbOyBu7UBNQytKq8WoaWwFAPD1uRjmbIkRHlYIGjoIxoZ9LyQ2qPO46CqaMyFEQ+nrcTHGZzDG+AyGtKMLhZXNyCtrQlmtGBV1LcgsakBnl6zHeTwuB1amhnAcLETocFu4DjGFt6M59PXoYyyifqhMCFEhvj4P3k4W8HayeHhMJmPQJu1Ce0cXpB1d4HI5EBrpw5DPU6v7Vgh5GioTQljG5XJgbKgHY0P6dSSai+5iIoQQojAqE0IIIQqjMiGEEKIwKhNCCCEKozIhhBCiMCoTQgghCtPpaxEV2XZVE7ds1XY0JuqJxkX99GdMejtHp5dTIYQQMjDoYy5CCCEKozIhhBCiMCoTQgghCqMyIYQQojAqE0IIIQqjMiGEEKIwKhNCCCEKozIhhBCiMCoTQgghCqMy+YPjx4/j2Wefhb+/P6ZNm4bDhw8/9fESiQQffvghQkNDERgYiJUrV6KoqEg1YXWEvGPyqM2bN2Pp0qXKC6fD5B2X2tpabNiwARMnTkRgYCDmzp2LU6dOqSitbpB3TGpqahATE4Pg4GCMHDkSf/7zn1FcXNyv56YyecSpU6cQExOD0NBQfPvttxgzZgzeeecdnD59+onnrFu3DqdPn0ZMTAw2b96M6upqLFmyBPfu3VNhcu3VnzF5YPfu3fjxxx9VkFL3yDsuUqkUK1asQEpKCl5//XVs3boVfn5+WLt2LY4fP67i9NpJ3jFpb2/HihUrcOvWLfztb3/DF198gZqaGixatAjNzc3yB2DIQ5GRkczatWu7HfvrX//KTJ069bGPv3btGuPl5cUkJiY+PFZfX88EBAQw27ZtU2pWXSHvmDAMw1RVVTFvvPEGM3ToUGbUqFHMyy+/rOSUukfecTl37hzj5eXFZGRkdDu+fPlyZtasWUrLqUvkHZNTp04xXl5ezK1btx4eKy0tZby8vJj9+/fL/fz0zuS+0tJSlJSUYPLkyd2OT5kyBQUFBSgtLe1xTnJyMgQCAUJDQx8es7S0RFBQEJKSkpSeWdv1Z0wA4Msvv0RmZiZ27NgBHx8fVUTVKf0ZF4FAgOjoaAwfPrzbcTc3N5SUlCg1ry7oz5iEhYUhNjYWfn5+D4/p6+sD+P2dpLyoTO4rKCgAALi6unY77uzsDAAoLCx87DnOzs7g8Xjdjjs5OT328UQ+/RkTAFixYgVOnDiBcePGKTegjurPuAQHB+Ojjz4Ch/O/Zcw7OjqQmJgIT09PJabVDf0ZE6FQiFGjRgH4fSyys7Oxfv16mJubIyoqSu4MOr2fyaMezHEIhcJuxwUCAQBALBb3OEcsFvd4/INzHvd4Ip/+jAkAeHh4KDeYjuvvuPzR559/jqKiInz77bcDG1AHKTomr732Gi5cuAAul4uNGzdi0KBBcmegMrmPub+ty6OvnB49zuX2fBPHPGUrmMc9nsinP2NClE/RcWEYBp999hl27tyJ5cuXIzIyUjlBdYiiY7Jy5Uq8/PLLOHr0KN59910AwNy5c+XKQGVyn4mJCYCeDS6RSLp9/VFCoRBlZWU9jkskkse+YyHy6c+YEOVTZFykUinWr1+PEydOYPny5Xj77beVF1SHKPq78uDjruDgYJSXl2Pbtm1ylwm9tLvvwWeNf5wMfHDN9R8/i3xwrLS0tMc7lOLi4sc+nsinP2NClK+/4yIWi/HKK6/g1KlTeO+996hIBlB/xiQzMxMnTpzocdzX1xc1NTVyZ6Ayuc/Z2RkODg49rsk+e/YsXFxcMGTIkB7nhIWFobm5GSkpKQ+PiUQipKWlISQkROmZtV1/xoQoX3/GpaurC3/605+QkZGBf/zjH3j55ZdVFVcn9GdMUlNT8eabb3YroK6uLqSmpsLLy0vuDLwPPvjgA7nP0lImJib497//jYaGBnA4HOzYsQOHDh3C+++/D09PT4hEIuTk5EAoFILP58Pe3h5Xr15FbGwszM3NUVFRgffeew8Mw+CTTz6BoaEh2z+SxpN3TP7o0KFD4HK5mD17NgvptZe84xIXF4fY2Fi88MILGDNmDKqqqh7+V11dDVtbW7Z/JI0n75i4urrixIkTOHv2LKysrFBWVoZNmzYhPT0dn376KRwcHOQLIPedKVouLi6OiYqKYvz8/Jhp06Yxhw4devi1gwcPMl5eXkxqaurDY42Njcz69euZ0aNHMyNHjmRWrlzJ3L17l43oWkveMXnUokWL6KZFJZFnXBYvXsx4eXk99j8fHx+2fgStI+/vSllZGbN27VomODiY8ff3ZxYtWsRcu3atX8/NYZinXJJECCGE9AHNmRBCCFEYlQkhhBCFUZkQQghRGJUJIYQQhVGZEEIIURiVCSGEEIVRmRCiRi5duoTFixcjMDAQ48aNw0cffYT29na2YxHSKyoTQtTEjz/+iBUrVsDGxgbvvvsuJk6ciD179mDjxo1sRyOkV3TTIiFqICUlBcuWLcNbb72F5cuXPzy+fPlyXLlyBampqbQSNVFr9M6EEJbJZDJs3LgRw4YNw7Jly7p9bezYsejo6EBubi5L6QjpGyoTQlh26dIl5OfnY/HixT02N3qwJ/eDnfQIUVe0ORYhLDt16hR4PB5Gjx4NkUjU7Wt1dXUA/rf9KiHqisqEEJZduXIFXV1dT92+1tHRUYWJCJEflQkhLBKJRKioqEBUVBQWLFjQ4+tr164Fn8/H4MGDWUhHSN9RmRDCorKyMgDA8OHDe+zOWVpaiqamJsyYMYONaITIhSbgCWGRRCIB8Pg5kTNnzgAApk+frtJMhPQHlQkhLHpw74hYLO52XCqVIi4uDq6urggPD2chGSHyoTIhhEUeHh4wMjLC5cuXux3/8ssvUV5ejg0bNoDH47GUjpC+ozkTQlhkZGSEefPmYdeuXYiJicGYMWOQlJSEc+fO4e2330ZYWBjbEQnpE1pOhRCWSaVSfPbZZzh27Bja2trg6+uL1atXY/z48WxHI6TPqEwIIYQojOZMCCGEKIzKhBBCiMKoTAghhCiMyoQQQojCqEwIIYQojMqEEEKIwqhMCCGEKIzKhBBCiMKoTAghhCiMyoQQQojC/j9oSaDolgrZfwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import mean_absolute_error\n",
    "\n",
    "thetas = np.linspace(0, 0.3, 101)\n",
    "errors = [\n",
    "    mean_absolute_error(data['tip'], data['total_bill'] * theta)\n",
    "    for theta in thetas\n",
    "]\n",
    "plt.plot(thetas, errors)\n",
    "plt.xlabel(r'$\\theta$')\n",
    "plt.ylabel('MAE')\n",
    "fig = plt.gcf()\n",
    "fig.savefig(\"MAE_vs_theta.png\", dpi=300, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = np.linspace(0.149, 0.15, 100)\n",
    "errors = [\n",
    "    mean_absolute_error(data['tip'], data['total_bill'] * theta)\n",
    "    for theta in thetas\n",
    "]\n",
    "plt.plot(thetas, errors)\n",
    "plt.xlabel(r'$\\theta$')\n",
    "plt.ylabel('MAE')\n",
    "fig = plt.gcf()\n",
    "fig.savefig('MAE_vs_theta_zoomed.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = np.linspace(0.149, 0.150, 100)\n",
    "np.gradient(errors)\n",
    "plt.plot(thetas, np.gradient(errors))\n",
    "plt.xlabel(r'$\\theta$')\n",
    "plt.ylabel('MAE')\n",
    "fig = plt.gcf()\n",
    "fig.savefig('MAE_deriv_vs_theta_zoomed.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = np.linspace(0.1435, 0.144, 100)\n",
    "errors = [\n",
    "    mean_squared_error(data['tip'], data['total_bill'] * theta)\n",
    "    for theta in thetas\n",
    "]\n",
    "plt.plot(thetas, errors)\n",
    "plt.xlabel(r'$\\theta$')\n",
    "plt.ylabel('MSE')\n",
    "fig = plt.gcf()\n",
    "fig.savefig(\"MSE_vs_theta_zoomed.png\", dpi=300, bbox_inches=\"tight\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def l1_loss(est, y_obs):\n",
    "    return np.abs(est - y_obs)\n",
    "\n",
    "\n",
    "thetas = np.linspace(0, 20, 200)\n",
    "loss = l1_loss(thetas, np.array([10]))\n",
    "plt.plot(thetas, loss, label='L1 Loss')\n",
    "plt.xlabel(r'Prediction')\n",
    "plt.ylabel(r'Loss')\n",
    "plt.vlines(np.array([10]), 0, 1, colors='r', label='Actual Value')\n",
    "plt.legend()\n",
    "fig = plt.gcf()\n",
    "fig.savefig('L1_loss_one_pt.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def l2_loss(est, y_obs):\n",
    "    return (est - y_obs)**2\n",
    "\n",
    "\n",
    "thetas = np.linspace(0, 20, 200)\n",
    "loss = l2_loss(thetas, np.array([10]))\n",
    "plt.plot(thetas, loss, label='L2 Loss')\n",
    "plt.vlines(np.array([10]), 0, 10, colors='r', label='Actual Value')\n",
    "plt.xlabel(r'Prediction')\n",
    "plt.ylabel(r'Loss')\n",
    "plt.legend()\n",
    "fig = plt.gcf()\n",
    "fig.savefig('L2_loss_one_pt.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def huber_loss(est, y_obs, alpha=1):\n",
    "    d = np.abs(est - y_obs)\n",
    "    return np.where(d < alpha, (est - y_obs)**2 / 2, alpha * (d - alpha / 2))\n",
    "\n",
    "\n",
    "thetas = np.linspace(0, 20, 200)\n",
    "loss = huber_loss(thetas, np.array([10]))\n",
    "plt.plot(thetas, loss, label='Huber Loss')\n",
    "plt.vlines(np.array([10]), 0, 1, colors='r', label='Actual Value')\n",
    "plt.xlabel(r'Prediction')\n",
    "plt.ylabel(r'Loss')\n",
    "plt.legend()\n",
    "fig = plt.gcf()\n",
    "fig.savefig('Huber_loss_one_pt.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = np.linspace(0, 20, 200)\n",
    "loss = huber_loss(thetas, np.array([10]), alpha=10)\n",
    "plt.plot(thetas, loss, label='Huber Loss')\n",
    "plt.vlines(np.array([10]), 0, 5, colors='r', label='Actual Value')\n",
    "plt.xlabel(r'Prediction')\n",
    "plt.ylabel(r'Loss')\n",
    "plt.legend()\n",
    "fig = plt.gcf()\n",
    "fig.savefig('Huber_loss_one_pt_alpha_ten.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thetas = np.linspace(0, 20, 200)\n",
    "loss = huber_loss(thetas, np.array([10]), alpha=0.1)\n",
    "plt.plot(thetas, loss, label='Huber Loss')\n",
    "plt.vlines(np.array([10]), 0, 0.1, colors='r', label='Actual Value')\n",
    "plt.xlabel(r'Prediction')\n",
    "plt.ylabel(r'Loss')\n",
    "plt.legend()\n",
    "fig = plt.gcf()\n",
    "fig.savefig('Huber_loss_one_pt_alpha_tenth.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 447.884x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.lmplot(x='total_bill', y='tip', hue='smoker', data=data)\n",
    "fig = plt.gcf()\n",
    "fig.savefig('two_condition_seaborn.png', dpi=300, bbox_inches='tight')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1d304551048>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.regplot(x=\"total_bill\", y=\"tip\", data=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   total_bill   tip\n",
       "0       16.99  1.01\n",
       "1       10.34  1.66\n",
       "2       21.01  3.50\n",
       "3       23.68  3.31\n",
       "4       24.59  3.61"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## make a copy of the data frame with only bill and tip\n",
    "loss_example = pd.DataFrame(data[[\"total_bill\", \"tip\"]])\n",
    "loss_example.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>prediction</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "      <td>2.442005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "      <td>1.486188</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "      <td>3.019807</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "      <td>3.403571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "      <td>3.534367</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   total_bill   tip  prediction\n",
       "0       16.99  1.01    2.442005\n",
       "1       10.34  1.66    1.486188\n",
       "2       21.01  3.50    3.019807\n",
       "3       23.68  3.31    3.403571\n",
       "4       24.59  3.61    3.534367"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## add predictions to dataframe\n",
    "loss_example[\"prediction\"] = lm.predict(\n",
    "    loss_example[\"total_bill\"].values.reshape(-1, 1))\n",
    "loss_example.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>total_bill</th>\n",
       "      <th>tip</th>\n",
       "      <th>prediction</th>\n",
       "      <th>loss</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>16.99</td>\n",
       "      <td>1.01</td>\n",
       "      <td>2.442005</td>\n",
       "      <td>2.050638</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>10.34</td>\n",
       "      <td>1.66</td>\n",
       "      <td>1.486188</td>\n",
       "      <td>0.030211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>21.01</td>\n",
       "      <td>3.50</td>\n",
       "      <td>3.019807</td>\n",
       "      <td>0.230585</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>23.68</td>\n",
       "      <td>3.31</td>\n",
       "      <td>3.403571</td>\n",
       "      <td>0.008756</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>24.59</td>\n",
       "      <td>3.61</td>\n",
       "      <td>3.534367</td>\n",
       "      <td>0.005720</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   total_bill   tip  prediction      loss\n",
       "0       16.99  1.01    2.442005  2.050638\n",
       "1       10.34  1.66    1.486188  0.030211\n",
       "2       21.01  3.50    3.019807  0.230585\n",
       "3       23.68  3.31    3.403571  0.008756\n",
       "4       24.59  3.61    3.534367  0.005720"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## compute the loss for each\n",
    "loss_example[\"loss\"] = (loss_example[\"tip\"] - loss_example[\"prediction\"])**2\n",
    "loss_example.head(5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1781161154513171"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## compute the average loss\n",
    "np.mean(loss_example[\"loss\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1781161154513171"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "## or we can do this in just one line of code using sklearn.metrics\n",
    "from sklearn.metrics import mean_squared_error\n",
    "mean_squared_error(data['tip'],\n",
    "                   lm.predict(data['total_bill'].values.reshape(-1, 1)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.0777683729508194"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(data['tip'], data['total_bill'] * 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2668192650409837"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(data['tip'], data['total_bill'] * 0.13)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.18466755852459"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(data['tip'], data['total_bill'] * 0.14)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.196598183401639"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(data['tip'], data['total_bill'] * 0.15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.178872579538934"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(data['tip'], data['total_bill'] * 0.145)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1831403511422127"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_squared_error(data['tip'], data['total_bill'] * 0.147)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the plot above, we see that the loss is minimized for $\\theta$ around 0.14. Indeed, scikit-learn computes the value by effectively traversing down the curve shown above. This can be done using a calculus based technique called \"gradient descent\" that we will not discuss in detail."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.778321963114754"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(data['tip'], data['total_bill'] * 0.1437)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7707192622950819"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(data['tip'], data['total_bill'] * 0.15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.7755313524590164"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mean_absolute_error(data['tip'], data['total_bill'] * 0.145)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "HuberRegressor(alpha=0.0001, epsilon=1, fit_intercept=False, max_iter=100,\n",
       "               tol=1e-05, warm_start=False)"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_huber = linear_model.HuberRegressor(epsilon=1, fit_intercept=False)\n",
    "features = data[[\"total_bill\"]]\n",
    "tip = data[\"tip\"]\n",
    "f_huber.fit(features, tip)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.14958863])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_huber.coef_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### For very small epsilon, we are fitting something close to L1 loss.\n",
    "### For very large epsilon, we are effectively fitting L2 loss."
   ]
  }
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